We study $AdS_5\times Σ_2$ and $AdS_4\times Σ_3$ solutions of $N=2$, $SO(4)$ gauged supergravity in seven dimensions with $Σ_{2,3}$ being $S^{2,3}$ or $H^{2,3}$. The $SO(4)$ gauged supergravity is obtained from coupling three vector multiplets to the pure $N=2$, $SU(2)$ gauged supergravity. With a topological mass term for the 3-form field, the $SO(4)\sim SU(2)\times SU(2)$ gauged supergravity admits two supersymmetric $AdS_7$ critical points, with $SO(4)$ and $SO(3)$ symmetries, provided that the two $SU(2)$ gauge couplings are different. These vacua correspond to $N=(1,0)$ superconformal field theories (SCFTs) in six dimensions. In the case of $Σ_2$, we find a class of $AdS_5\times S^2$ and $AdS_5\times H^2$ solutions preserving eight supercharges and $SO(2)\times SO(2)$ symmetry, but only $AdS_5\times H^2$ solutions exist for $SO(2)$ symmetry. These should correspond to some $N=1$ four-dimensional SCFTs. We also give RG flow solutions from the $N=(1,0)$ SCFTs in six dimensions to these four-dimensional fixed points including a two-step flow from the $SO(4)$ $N=(1,0)$ SCFT to the $SO(3)$ $N=(1,0)$ SCFT that eventually flows to the $N=1$ SCFT in four dimensions. For $AdS_4\timesΣ_3$, we find a class of $AdS_4\times S^3$ and $AdS_4\times H^3$ solutions with four supercharges, corresponding to $N=1$ SCFTs in three dimensions. When the two $SU(2)$ gauge couplings are equal, only $AdS_4\times H^3$ are possible. The uplifted solutions for equal $SU(2)$ gauge couplings to eleven dimensions are also given.
We study holographic renormalization group flows from four-dimensional $\mathcal{N}=2$ SCFTs to either $\mathcal{N}=2$ or $\mathcal{N}=1$ SCFTs. Our approach is based on the framework of five-dimensional half-maximal supergravity with general gauging, which we use to study domain wall solutions interpolating between different supersymmetric AdS$_5$ vacua. We show that a holographic RG flow connecting two $\mathcal{N}=2$ SCFTs is only possible if the flavor symmetry of the UV theory admits an ${\rm SO}(3)$ subgroup. In this case the ratio of the IR and UV central charges satisfies a universal r…
We study certain N=1 preserving deformations of four-dimensional N=2 superconformal field theories (SCFTs) with non-abelian flavor symmetry. The deformation is described by adding an N=1 chiral multiplet transforming in the adjoint representation of the flavor symmetry with a superpotential coupling, and giving a nilpotent vacuum expectation value to the chiral multiplet which breaks the flavor symmetry. This triggers a renormalization group flow to an infrared SCFT. Remarkably, we find classes of theories flow to enhanced N=2 supersymmetric fixed points in the infrared under the deformation. …
We continue to investigate the $\mathcal{N}=1$ deformations of four-dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs) labeled by a nilpotent element of the flavor symmetry. This triggers a renormalization group (RG) flow to an $\mathcal{N}=1$ SCFT. We systematically analyze all possible deformations of this type for certain classes of $\mathcal{N}=2$ SCFTs: conformal SQCDs, generalized Argyres-Douglas theories and the $E_6$ SCFT. We find a number of examples where the amount of supersymmetry gets enhanced to $\mathcal{N}=2$ at the end point of the RG flow. Most notably, we find…
We present the general form of all timelike supersymmetric solutions to 3D U(1)^3 gauged supergravity, a known consistent truncation of string theory. We uncover a rich vacuum structure, including an infinite class of new timelike-warped AdS_3 (Goedel) and timelike-warped dS_3 critical points. We outline the construction of supersymmetric flows, driven by irrelevant scalar operators in the SCFT, which interpolate between critical points. For flows from AdS_3 to Goedel, the natural candidate for the central charge decreases along the flow. Flows to timelike-warped dS_3 exhibit topology change.
This is the second in a series of three papers on systematic analysis of rank 1 Coulomb branch geometries of four dimensional $\mathcal{N}$=2 SCFTs. In the first paper we developed a strategy for classifying physical rank-1 CB geometries of $\mathcal{N}$=2 SCFTs. Here we show how to carry out this strategy computationally to construct the Seiberg-Witten curves and one-forms for all the rank-1 SCFTs. Explicit expressions are given for all cases, with the exception of the $N_f$=4 SU(2) gauge theory and the En SCFTs which were previously constructed. Our classification includes all known rank-1 t…
Following a recent proposal, we delineate a general procedure to classify 5d SCFTs via compactifications of 6d SCFTs on a circle (possibly with a twist by a discrete global symmetry). The path from 6d SCFTs to 5d SCFTs can be divided into two steps. The first step involves computing the Coulomb branch data of the 5d KK theory obtained by compactifying a 6d SCFT on a circle of finite radius. The second step involves computing the limit of the KK theory when the inverse radius along with some other mass parameters is sent to infinity. Under this RG flow, the KK theory reduces to a 5d SCFT. We il…
It is shown that certain extremal and next-to-extremal n-point correlators in four-dimensional N=2 superconformal field theories are free. These results hold for any gauge group.
Using the F-theory realization, we identify a subclass of 6d (1,0) SCFTs whose compactification on a Riemann surface leads to N = 1 4d SCFTs where the moduli space of the Riemann surface is part of the moduli space of the theory. In particular we argue that for a special case of these theories (dual to M5 branes probing ADE singularities), we obtain 4d N = 1 theories whose space of marginal deformations is given by the moduli space of flat ADE connections on a Riemann surface.
We study AdS duals of four-dimensional (4D) $\mathcal{N}=1$ superconformal field theories (SCFTs) on $\mathbb{Z}_k$ S-folds with T-branes that flow to 4D $\mathcal{N}=3$ theories. In a previous study, it was discussed how considering T-brane structure breaks the $\mathcal{N}=2$ supersymmetry in 4D SCFTs on $\mathbb{Z}_k$ S-folds down to $\mathcal{N}=1$. In this study, we analyze this effect from the AdS perspective. We also discuss the constructions of 4D $\mathcal{N}=1$ SCFTs on S-folds with T-branes starting from global K3 hypersurfaces whose fibers involve complex multiplications. We choose…
We refine our previous proposal for systematically classifying 4d rank-1 $\mathcal N=2$ SCFTs by constructing their possible Coulomb branch geometries. Four new recently discussed rank-1 theories, including novel $\mathcal{N}=3$ SCFTs, sit beautifully in our refined classification framework. By arguing for the consistency of their RG flows we can make a strong case for the existence of at least four additional rank-1 SCFTs, nearly doubling the number of known rank-1 SCFTs. The refinement consists of relaxing the assumption that the flavor symmetries of the SCFTs have no discrete factors. This …
With the purpose of holographically describing flows from a large family of four dimensional ${\cal N}=1$ and ${\cal N}=2$ conformal field theories, we discuss truncations of seven dimensional supergravity to five dimensions. We write explicitly the reduced gauged supergravity and find BPS equations for simple configurations. Lifting these flows to eleven dimensions or Massive IIA supergravity, we present string duals to RG flows from strongly coupled conformal theories when deformed by marginal and/or relevant operators. We further discuss observables common to infinite families of ${\cal N}=…
We study 6d superconformal field theories (SCFTs) compactified on a circle with arbitrary twists. The theories obtained after compactification, often referred to as 5d Kaluza-Klein (KK) theories, can be viewed as starting points for RG flows to 5d SCFTs. According to a conjecture, all 5d SCFTs can be obtained in this fashion. We compute the Coulomb branch prepotential for all 5d KK theories obtainable in this manner and associate to these theories a smooth local genus one fibered Calabi-Yau threefold in which is encoded information about all possible RG flows to 5d SCFTs. These Calabi-Yau thre…
We study $N=2$ seven-dimensional gauged supergravity coupled to three vector multiplets with $SO(4)$ gauge group. The resulting gauged supergravity contains 10 scalars consisting of the dilaton and 9 vector multiplet scalars parametrized by $SO(3,3)/SO(3)\times SO(3)$ coset manifold. The maximally supersymmetric $AdS_7$ vacuum with unbroken $SO(4)$ symmetry is identified with a $(1,0)$ SCFT in six dimensions. We find one new supersymmetric $AdS_7$ critical point preserving $SO(3)_{\textrm{diag}}\subset SO(3)\times SO(3)\sim SO(4)$ and study a holographic RG flow interpolating between the $SO(4…
It is shown that certain extremal correlators in four-dimensional N=2 superconformal field theories (including N=4 super-Yang-Mills as a special case) have a free-field functional form. It is further argued that the coupling constant dependence receives no correction beyond the lowest order. These results hold for any finite value of N_c.
We present three infinite families of supersymmetric Type IIB backgrounds with AdS$_4$, AdS$_3$ and AdS$_2$ factors, dual to SCFTs in $3$, $2$ and $1$ space-time dimensions respectively. These field theories emerge at low energies, after a twisted compactification of a family of five dimensional ${\cal N}=2$ SCFTs on hyperbolic spaces. The holographic flows across dimensions are explicitly computed. We also discuss a family of SUSY breaking backgrounds, dual to a QCD-like quiver with massive (bi)fundamental matter. Some field theoretical observables are computed for these theories at the fixed…
We propose that a certain $4d$ $\mathcal{N}=1$ $SU(2)\times SU(2)$ gauge theory flows in the IR to an $\mathcal{N}=3$ SCFT plus a single free chiral field. The specific $\mathcal{N}=3$ SCFT has rank $1$ and a dimension three Coulomb branch operator. The flow is generically expected to land at the $\mathcal{N}=3$ SCFT deformed by the marginal deformation associated with said Coulomb branch operator. We also present a discussion about the properties expected of various RG invariant quantities from $\mathcal{N}=3$ superconformal symmetry, and use these to test our proposal. Finally, we discuss a …
In this paper we begin mapping out the space of rank-2 $\mathcal{N}=2$ superconformal field theories (SCFTs) in four dimensions. This represents an ideal set of theories which can be potentially classified using purely quantum field-theoretic tools, thus providing a precious case study to probe the completeness of the current understanding of SCFTs, primarily derived from string theory constructions. Here, we collect and systematize a large amount of field theoretic data characterizing each theory. We also provide a detailed description of each case and determine the theories' Coulomb, Higgs a…
We engineer a large new set of four-dimensional N=1 superconformal field theories by wrapping M5-branes on complex curves. We present new supersymmetric AdS_5 M-theory backgrounds which describe these fixed points at large N, and then directly construct the dual four-dimensional CFTs for a certain subset of these solutions. Additionally, we provide a direct check of the central charges of these theories by using the M5-brane anomaly polynomial. This is a companion paper which elaborates upon results reported in arXiv:1112:5487.
We study four-point functions of spinning operators in the flavor current multiplet in four dimensional $\mathcal{N}=2$ SCFTs, using superspace techniques. In particular we explicitly construct the differential operators relating the different components of the super-correlator. As a byproduct of our analysis, we report the computation of the four-point amplitudes of gluons in bosonic Yang-Mills theories on $\mathrm{AdS}_5$ and we give evidence of an AdS double copy relation between the gluon amplitude and its gravitational counterpart.
We find a large class of two-dimensional $\mathcal{N}=(0,2)$ SCFTs obtained by compactifying four-dimensional $\mathcal{N}=1$ quiver gauge theories on a Riemann surface. We study these theories using anomalies and $c$-extremization. The gravitational duals to these fixed points are new AdS$_3$ solutions of IIB supergravity which we exhibit explicitly. Along the way we uncover a universal relation between the conformal anomaly coefficients of four-dimensional and two-dimensional SCFTs connected by an RG flow across dimensions. We also observe an interesting novel phenomenon in which the superco…
Turning on N=2 supersymmetry-preserving relevant operators in a 4-dimensional N=2 superconformal field theory (SCFT) corresponds to a complex deformation compatible with the rigid special Kahler geometry encoded in the low energy effective action. Field theoretic consistency arguments indicate that there should be many distinct such relevant deformations of each SCFT fixed point. Some new supersymmetry-preserving complex deformations are constructed of isolated rank 1 SCFTs. We also make predictions for the dimensions of certain Higgs branches for some rank 1 SCFTs.
We study the consistency of four-point functions of half-BPS chiral primary operators of weight p in four-dimensional N=4 superconformal field theories. The resulting conformal bootstrap equations impose non-trivial bounds for the scaling dimension of unprotected local operators transforming in various representations of the R-symmetry group. These bounds generalize recent bounds for operators in the singlet representation, arising from consistency of the four-point function of the stress-energy tensor multiplet.
5d superconformal field theories (SCFTs) can be obtained from 6d SCFTs by circle compactification and mass deformation. Successive decoupling of hypermultiplet matter and RG-flow generates a decoupling tree of descendant 5d SCFTs. In this paper we determine the magnetic quivers and Hasse diagrams, that encode the Higgs branches of 5d SCFTs, for entire decoupling trees. Central to this undertaking is the approach in arXiv:2008.05577, which, starting from the generalized toric polygons (GTPs) dual to 5-brane webs/tropical curves, provides a systematic and succinct derivation of magnetic quivers …
Using the recently established classification of 6D SCFTs we present evidence for the existence of families of weak C-functions, that is, quantities which decrease in a flow from the UV to the IR. Introducing a background R-symmetry field strength R and a non-trivial tangent bundle T on the 6D spacetime, we consider C-functions given by the linear combinations C = m1 alpha + m2 beta + m3 gamma, where alpha, beta and gamma are the anomaly polynomial coefficients for the formal characteristic classes c2(R)^2, c2(R)p1(T) and p1(T)^2. By performing a detailed sweep over many theories, we determine…
We show that there is a family of two-dimensional $(0,2)$ SCFTs associated with twisted compactifications of the four-dimensional $\mathcal{N}=1$ Leigh-Strassler fixed point on a closed hyperbolic Riemann surface. We calculate the central charges for this class of theories using anomalies and $c$-extremization. In a suitable truncation of the five-dimensional maximal supergravity, we construct supersymmetric $AdS_3$ solutions that are holographic duals of those two-dimensional $(0,2)$ SCFTs. We also exhibit supersymmetric domain wall solutions that are holographically dual to the RG flows betw…
We construct a four supercharges Liouville superconformal field theory in four dimensions. The Liouville superfield is chiral and its lowest component is a log-correlated complex scalar whose real part carries a background charge. The action consists of a supersymmetric Paneitz operator, a background supersymmetric $\mathcal{Q}$-curvature charge and an exponential potential. It localizes semiclassically on solutions that describe curved superspaces with a constant complex supersymmetric $\mathcal{Q}$-curvature. The theory is non-unitary with a continuous spectrum of scaling dimensions. We stud…
We show that all known 6D SCFTs can be obtained iteratively from an underlying set of UV progenitor theories through the processes of "fission" and "fusion." Fission consists of a tensor branch deformation followed by a special class of Higgs branch deformations characterized by discrete and continuous homomorphisms into flavor symmetry algebras. Almost all 6D SCFTs can be realized as fission products. The remainder can be constructed via one step of fusion involving these fission products, whereby a single common flavor symmetry of decoupled 6D SCFTs is gauged and paired with a new tensor mul…
We describe the general BPS system that governs the gravity duals of N=(0,2) two-dimensional superconformal field theories in the low-energy limit of M5-branes on a four-manifold, M4. In order to preserve supersymmetry, we restrict to cases where the four-manifold is embedded in a Calabi-Yau fourfold that is a sum of two line bundles over M4. We further reduce the N=(0,2) system to describe the gravity duals of SCFTs with N=(0,4) and N=(2,2) supersymmetry. In the first case, the solutions fit in the larger class of AdS3xS2xCY3 solutions of M-theory dual to N=(0,4) SCFTs. In the case of the N=(…
We describe an infinite two-parameter subfamily of theories of class S where dialing one of the parameters interpolates between Gaiotto's T_N theory and a theory of N^2 free hypermultiplets. After using the reduced superconformal index to study the operator content, we use these theories to construct new N=1 SCFTs and then examine the flows between them.
We study four-dimensional $N=4$ gauged supergravity coupled to six vector multiplets with semisimple gauge groups $SO(4)\times SO(4)$, $SO(3,1)\times SO(3,1)$ and $SO(4)\times SO(3,1)$. All of these gauge groups are dyonically embedded in the global symmetry group $SO(6,6)$ via its maximal subgroup $SO(3,3)\times SO(3,3)$. For $SO(4)\times SO(4)$ gauge group, there are four $N=4$ supersymmetric $AdS_4$ vacua with $SO(4)\times SO(4)$, $SO(4)\times SO(3)$, $SO(3)\times SO(4)$ and $SO(3)\times SO(3)$ symmetries, respectively. These $AdS_4$ vacua correspond to $N=4$ SCFTs in three dimensions with …
We determine all 5d SCFTs upto rank three by studying RG flows of 5d KK theories. Our analysis reveals the existence of new rank one and rank two 5d SCFTs not captured by previous classifications. In addition to that, we provide for the first time a systematic and conjecturally complete classification of rank three 5d SCFTs. Our methods are based on a recently studied geometric description of 5d KK theories, thus demonstrating the utility of these geometric descriptions. It is straightforward, though computationally intensive, to extend this work and systematically classify 5d SCFTs of higher …
We study compactifications of an infinite family of four-dimensional $\mathcal{N}=1$ SCFTs on a Riemann surface in the presence of arbitrary background fluxes for global symmetries. The four-dimensional parent theories have holographic Sasaki-Einstein duals in type IIB string theory. We compute central charges and R-charges of baryonic operators in the resulting two-dimensional $\mathcal{N}=(0,2)$ theories in three distinct ways: from the field theory side utilizing c-extremization, its recently discovered geometric dual formulation, and holographically using new AdS$_3$ duals of two-dimension…
We study the holographic description of ${\cal N}=2$ Super Conformal Field Theories in four dimensions first given by Gaiotto and Maldacena. We present new expressions that holographically calculate characteristic numbers of the CFT and associated Hanany-Witten set-ups, or more dynamical observables, like the central charge. A number of examples of varying complexity are studied and some proofs for these new expressions are presented. We repeat this treatment for the case of the marginally deformed Gaiotto-Maldacena theories, presenting an infinite family of new solutions and compute some of i…
In this paper we introduce the characteristic dimension of a four dimensional $\mathcal{N}=2$ superconformal field theory, which is an extraordinary simple invariant determined by the scaling dimensions of its Coulomb branch operators. We prove that only nine values of the characteristic dimension are allowed, $-\infty$, 1 ,6/5, 4/3, 3/2, 2, 3, 4, and 6, thus giving a new organizing principle to the vast landscape of 4d $\mathcal N=2$ SCFTs. Whenever the characteristic dimension differs from 1 or 2, only very constrained special Kähler geometries (i.e. isotrivial, diagonal and rigid) are compa…
Applying the Casimir operator to four-point functions in CFTs allows us to find the conformal blocks for any external operators. In this work, we initiate the program to find the superconformal blocks, using the super Casimir operator, for $4D$ ${\mathcal N}=1$ SCFTs. We begin by finding the most general four-point function with zero $U(1)_R$-charge, including all the possible nilpotent structures allowed by the superconformal algebra. We then study particular cases where some of the operators satisfy shortening conditions. Finally, we obtain the super Casimir equations for four point-function…
We study lower bounds on the minimal distance in theory space between four-dimensional superconformal field theories (SCFTs) connected via broad classes of renormalization group (RG) flows preserving various amounts of supersymmetry (SUSY). For N=1 RG flows, the ultraviolet (UV) and infrared (IR) endpoints of the flow can be parametrically close. On the other hand, for RG flows emanating from a maximally supersymmetric SCFT, the distance to the IR theory cannot be arbitrarily small regardless of the amount of (non-trivial) SUSY preserved along the flow. The case of RG flows from N=2 UV SCFTs i…
The partition function of four-dimensional N=2 superconformal field theories on S^4 computes the exact Kahler potential on the space of exactly marginal couplings [1]. We present a new elementary proof of this result using supersymmetry Ward identities. The partition function is a section rather than a function, and is subject to ambiguities coming from Kahler transformations acting on the Kahler potential. This ambiguity is realized by a local supergravity counterterm in the underlying SCFT. We provide an explicit construction of the Kahler ambiguity counterterm in the four dimensional N=2 of…
We study a rich set of four-dimensional $\mathcal{N}=1$ superconformal field theories (SCFTs) with both central charges identical: $a = c$. We construct them via the diagonal $\mathcal{N}=1$ gauging of the flavor symmetry $G$ of a collection of $\mathcal{N}=2$ Argyres--Douglas theories of type $\mathcal{D}_p(G)$, with or without additional adjoint chiral multiplets. In this way, we construct infinitely-many theories that flow to interacting SCFTs with $a = c$ in the infrared. Finally, we briefly highlight the features of the SCFTs without $a = c$ that arise from generalizing this construction.
We construct a Liouville superconformal field theory with eight real supercharges in four dimensions. The Liouville superfield is an $\mathcal{N}=2$ chiral superfield with sixteen bosonic and sixteen fermionic component fields. Its lowest component is a log-correlated complex scalar field whose real part carries a background charge. The theory is non-unitary with a continuous spectrum of scaling dimensions. We study its quantum dynamics on the supersymmetric 4-sphere and show that the classical background charge is not corrected quantum mechanically. We calculate the super-Weyl anomaly coeffic…
$N$ M5-branes probing the intersection between the orbifold $\mathbb{C}^2/Γ_\text{ADE}$ and an $E_8$ wall give rise to 6d $(1,0)$ SCFTs known as ADE-type orbi-instantons. At fixed $N$ and order of the orbifold, each element of $\text{Hom}(Γ_\text{ADE},E_8)$ defines a different SCFT. The SCFTs are connected by Higgs branch RG flows, which generically reduce the flavor symmetry of the UV fixed point. We determine the full hierarchy of these RG flows for type A, i.e. $\mathbb{C}^2/\mathbb{Z}_k$, for any value of $N$ and $k$. The hierarchy takes the form of an intricate Hasse diagram: each node re…
In this work we construct the crossing symmetry equations for mixed correlators of two long and two BPS operators in 4D $\mathcal{N}=1$ SCFTs. The analysis presented here illustrates how our general group theoretic approach to long superblocks and tensor structures of superconformal algebras can be applied to give explicit ready-to-use expressions. In the case at hand, we obtain a system of four crossing symmetry equations for the relevant OPE coefficients. One of these four equations coincides with the equation found and analysed by Li, Meltzer and Stergiou by restricting to the superprimary …
By analyzing SU(3)xU(1) invariant stationary point, studied earlier by Nicolai and Warner, of gauged N=8 supergravity, we find that the deformation of S^7 gives rise to nontrivial renormalization group flow in a three-dimensional boundary super conformal field theory from N=8, SO(8) invariant UV fixed point to N=2, SU(3)xU(1) invariant IR fixed point. By explicitly constructing 28-beins u, v fields, that are an element of fundamental 56-dimensional representation of E_7, in terms of scalar and pseudo-scalar fields of gauged N=8 supergravity, we get A_1, A_2 tensors. Then we identify one of the…
We study a recently-found class of RG flows in four dimensions exhibiting enhancement of supersymmetry in the infrared, which provides a lagrangian description of several strongly-coupled N=2 SCFTs. The procedure involves starting from a N=2 SCFT, coupling a chiral multiplet in the adjoint representation of the global symmetry to the moment map of the SCFT and turning on a nilpotent expectation value for this chiral. In this note we show that, combining considerations based on 't Hooft anomaly matching and basic results about the N=2 superconformal algebra, it is possible to understand in deta…
Supersymmetric and non-supersymmetric deformations of large $N=(4,4)$ SCFT with superconformal symmetry $D^1(2,1;α)\times D^1(2,1;α)$ are explored in the gravity dual described by a Chern-Simons $N=8$, $(SO(4)\times SO(4))\ltimes \mathbf{T}^{12}$ gauged supergravity in three dimensions. For $α>0$, the gauged supergravity describes an effective theory of the maximal supergravity in nine dimensions on $AdS_3\times S^3\times S^3$ with the parameter $α$ being the ratio of the two $S^3$ radii. We consider the scalar manifold of the supergravity theory of the form $SO(8,8)/SO(8)\times SO(8)$ and fin…
We provide explicit solutions of Type IIA supergravity which are believed to be dual to N = 2 superconformal four dimensional gauge theories. These explicit solutions are based on the general ansatz for such a type of backgrounds introduced by Gaiotto and Maldacena.
Detailed studies of four dimensional N=2 superconformal field theories (SCFT) defined by isolated complete intersection singularities are performed: we compute the Coulomb branch spectrum, Seiberg-Witten solutions and central charges. Most of our theories have exactly marginal deformations and we identify the weakly coupled gauge theory descriptions for many of them, which involve (affine) D and E shaped quiver gauge theories and theories formed from Argyres-Douglas matters. These investigations provide strong evidence for the singularity approach in classifying 4d N=2 SCFTs.
We introduce a class of Higgs-branch RG flows in theories of class-S, which flow between $d=4$ $\mathcal{N}=2$ SCFTs of the same ADE type. We discuss two applications of this class of RG flows: 1) determining the current-algebra levels in SCFTs where they were previously unknown - a program we carry out for the class-S theories of type $E_6$ and $E_7$ - and 2) constructing a multitude of examples of pairs of $\mathcal{N}=2$ SCFTs whose "conventional invariants" coincide. We disprove the conjecture of [1] that the global form of the flavour symmetry group is a reliable diagnostic for determinin…
We construct a continuous one parameter family of $AdS_4\times S^1\times S^5$ S-fold solutions of type IIB string theory which have nontrivial $SL(2,\mathbb{Z})$ monodromy in the $S^1$ direction. The solutions span a subset of a conformal manifold that contains the known $\mathcal{N}=4$ S-fold SCFT in $d=3$, and generically preserve $\mathcal{N}=2$ supersymmetry. We also construct RG flows across dimensions, from $AdS_5\times S^5$, dual to $\mathcal{N}=4$, $d=4$ SYM compactified with a twisted spatial circle, to various $AdS_4\times S^1\times S^5$ S-fold solutions, dual to $d=3$ SCFTs. We cons…
We study a class of four-dimensional N=1 superconformal field theories obtained by wrapping M5-branes on a Riemann surface with punctures. We identify UV descriptions of four-dimensional SCFTs corresponding to curves with a class of punctures. The quiver tails appearing in these UV descriptions differ significantly from their N=2 counterpart. We find a new type of object that we call the `Fan'. We show how to construct new N=1 superconformal theories using the Fan. Various dual descriptions for these SCFTs can be identified with different colored pair-of-pants decompositions. For example, we f…
We apply recently developed tools from exceptional field theory to calculate the full Kaluza-Klein spectrum of the AdS$_5$ Pilch-Warner solution of type IIB supergravity. Through the AdS/CFT correspondence this yields detailed information about the spectrum of protected and unprotected operators of the four-dimensional $\mathcal{N}=1$ Leigh-Strassler SCFT, in the planar limit. We also calculate explicitly the superconformal index of the SCFT in this limit and show that it agrees precisely with the spectrum of protected operators in the supergravity calculation.
Any N=2 superconformal field theory (SCFT) in four dimensions has a sector of operators related to a two-dimensional chiral algebra containing a Virasoro sub-algebra. Moreover, there are well-known examples of isolated SCFTs whose chiral algebra is a Virasoro algebra. In this note, we consider the chiral algebras associated with interacting N=2 SCFTs possessing an exactly marginal deformation that can be interpreted as a gauge coupling (i.e., at special points on the resulting conformal manifolds, free gauge fields appear that decouple from isolated SCFT building blocks). At any point on these…
We propose Type IIB 5-brane configurations that engineer the 6d $\mathcal{N}=(1,0)$ SCFTs with $SO(N)$ gauge symmetry coupled to a single tensor multiplet on a circle, by considering RG flows on Higgs branches of $D$-type conformal matter theories. We test the brane systems against known Calabi-Yau threefolds for the 6d SCFTs on a circle. In addition we study a new RG flow involving Higgs vevs of scalar operators with Kaluza-Klein momentum along the circle. The new RG flow results in the 5-brane webs for the 6d SCFTs of $D_N$ gauge symmetry compactified on a circle with $Z_2$ outer-automorphis…
We study a rich set of four-dimensional superconformal field theories (SCFTs) with both central charges identical: $a = c$. These are constructed via the diagonal $\mathcal{N}=2$ or $\mathcal{N}=1$ gauging of the flavor symmetry $G$ of a collection of $\mathcal{N}=2$ Argyres-Douglas theories of type $\mathcal{D}_p(G)$, with or without adjoint chiral multiplets, in arXiv:2106.12579 and arXiv:2111.12092. We compute superconformal indices of some theories where the rank of $G$ is low, performing a refined test for unitarity, and further determine the relevant and marginal operator content in deta…
We explore consequences of the Averaged Null Energy Condition (ANEC) for scaling dimensions $Δ$ of operators in four-dimensional $\mathcal{N}=1$ superconformal field theories. We show that in many cases the ANEC bounds are stronger than the corresponding unitarity bounds on $Δ$. We analyze in detail chiral operators in the $(\frac12 j,0)$ Lorentz representation and prove that the ANEC implies the lower bound $Δ\ge\frac32j$, which is stronger than the corresponding unitarity bound for $j>1$. We also derive ANEC bounds on $(\frac12 j,0)$ operators obeying other possible shortening conditions, as…
We consider 4d N=1 SCFTs, topologically twisted on compact constant curvature Riemann surfaces, giving rise to 2d N=(0,2) SCFTs. The exact R-current of these 2d SCFT extremizes the central charge c_{2d}, similarly to the 4d picture, where the exact R-current maximizes the central charge a_{4d}. There are global currents that do not mix with the R-current in 4d but their mixing becomes non trivial in 2d. In this paper we study the holographic dual of this process by analyzing a 5d N=2 truncation of T^{1,1} with one Betti vector multiplet, dual to the baryonic current on the CFT side. The hologr…
We analyse the critical behaviour of anomalous currents in N=1 four-dimensional supersymmetric gauge theories in the context of electric-magnetic duality. We show that the anomalous dimension of the Konishi superfield is related to the slope of the beta function at the critical point. We construct a duality map for the Konishi current in the minimal SQCD. As a byproduct we compute the slope of the beta function in the strong coupling regime. We note that the OPE of the stress tensor with itself does not close, but mixes with the Konishi operator. As a result in superconformal theories in four …
With the eventual aim of classifying renormalization group flows between 6D superconformal field theories (SCFTs), we study flows generated by the vevs of "conformal matter," a generalization of conventional hypermultiplets which naturally appear in the F-theory classification of 6D SCFTs. We consider flows in which the parent UV theory is (on its partial tensor branch) a linear chain of gauge groups connected by conformal matter, with one flavor group G at each end of the chain, and in which the symmetry breaking of the conformal matter at each end is parameterized by the orbit of a nilpotent…
We consider Alday-Gaiotto-Tachikawa (AGT) realization of the Nekrasov partition function of N=2 SCFT. We focus our attention on the SU(2) theory with N_f=4 flavor symmetry, whose partition function, according to AGT, is given by the Liouville four-point function on the sphere. The gauge theory with N_f=4 is known to exhibit SO(8) symmetry. We explain how the Weyl symmetry transformations of SO(8) flavor symmetry are realized in the Liouville theory picture. This is associated to functional properties of the Liouville four-point function that are a priori unexpected. In turn, this can be though…
We consider four-dimensional N=2 superconformal field theories based on ADE quiver diagrams. We use the procedure of hep-th/0206079 and compute the exact anomalous dimensions of operators with large U(1)_R charge to all orders in perturbation in the planar limit. The results are in agreement with the string computation in the dual pp-wave backgrounds.
