Compactifications of 6d N=(1,0) SCFTs give rise to new 4d N=1 SCFTs and shed light on interesting dualities between such theories. In this paper we continue exploring this line of research by extending the class of compactified 6d theories to the D-type case. The simplest such 6d theory arises from D5 branes probing D-type singularities. Equivalently, this theory can be obtained from an F-theory compactification using "-2"-curves intersecting according to a D-type quiver. Our approach is two-fold. We start by compactifying the 6d SCFT on a Riemann surface and compute the central charges of the resulting 4d theory by integrating the 6d anomaly polynomial over the Riemann surface. As a second step, in order to find candidate 4d UV Lagrangians, there is an intermediate 5d theory that serves to construct 4d domain walls. These can be used as building blocks to obtain torus compactifications. In contrast to the A-type case, the vanishing of anomalies in the 4d theory turns out to be very restrictive and constraints the choices of gauge nodes and matter content severely. As a consequence, in this paper one has to resort to non-maximal boundary conditions for the 4d domain walls. However, the comparison to the 6d theory compactified on the Riemann surface becomes less tractable.
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…
A large class of 5d superconformal field theories (SCFTs) can be constructed by integrating out BPS particles from 6d SCFTs compactified on a circle. We describe a general method for extracting the flavor symmetry of any 5d SCFT lying in this class. For this purpose, we utilize the geometric engineering of 5d N=1 theories in M-theory, where the flavor symmetry is encoded in a collection of non-compact surfaces.
We construct a new class of supersymmetric $AdS_3\times Y_7$ solutions of type IIB supergravity, where $Y_7$ is an $S^5$ fibration over a spindle, which are dual to $d=2$, $\mathcal{N}=(0,2)$ SCFTs. The solutions are constructed in a sub-truncation of $D=5$, $SO(6)$ maximal gauged supergravity and they all lie within the anti-twist class. We show that the central charge computed from the gravity solutions agrees with an anomaly polynomial calculation associated with compactifying the $\mathcal{N}=1$, $d=4$ Leigh-Strassler SCFT on a spindle.
According to a conjecture, all 5d SCFTs should be obtainable by rank-preserving RG flows of 6d SCFTs compactified on a circle possibly twisted by a background for the discrete global symmetries around the circle. For a 6d SCFT admitting an F-theory construction, its untwisted compactification admits a dual M-theory description in terms of a "parent" Calabi-Yau threefold which captures the Coulomb branch of the compactified 6d SCFT. The RG flows to 5d SCFTs can then be identified with a sequence of flop transitions and blowdowns of the parent Calabi-Yau leading to "descendant" Calabi-Yau threef…
We study compactifications of $6d$ non minimal $(D_{p+3},D_{p+3})$ type conformal matter. These can be described by $N$ M5-branes probing a $D_{p+3}$-type singularity. We derive $4d$ Lagrangians corresponding to compactifications of such $6d$ SCFTs on three punctured spheres (trinions) with two maximal punctures and one minimal puncture. The trinion models are described by simple $\mathcal{N}=1$ quivers with $SU(2N)$ gauge nodes. We derive the trinion Lagrangians using RG flows between the aforementioned $6d$ SCFTs with different values of $p$ and their relations to matching RG flows in their …
We compute the partition function for 6d $\mathcal{N}=1$ $SO(2N)$ gauge theories compactified on a circle with $\mathbb{Z}_2$ outer automorphism twist. We perform the computation based on 5-brane webs with two O5-planes using topological vertex with two O5-planes. As representative examples, we consider 6d $SO(8)$ and $SU(3)$ gauge theories with $\mathbb{Z}_2$ twist. We confirm that these partition functions obtained from the topological vertex with O5-planes indeed agree with the elliptic genus computations.
We classify 5d N=1 gauge theories carrying a simple gauge group that can arise by mass-deforming 5d SCFTs and 6d SCFTs (compactified on a circle, possibly with a twist). For theories having a 6d UV completion, we determine the tensor branch data of the 6d SCFT and capture the twist in terms of the tensor branch data. We also determine the dualities between these 5d gauge theories, thus determining the sets of gauge theories having a common UV completion.
We consider all 4d $\mathcal{N}=2$ theories of class $\mathcal{S}$ arising from the compactification of exceptional 6d $(2,0)$ SCFTs on a three-punctured sphere with a simple puncture. We find that each of these 4d theories has another origin as a 6d $(1,0)$ SCFT compactified on a torus, which we check by identifying and comparing the central charges and the flavor symmetry. Each 6d theory is identified with a complex structure deformation of $(\mathfrak{e}_n,\mathfrak{e}_n)$ minimal conformal matter, which corresponds to a Higgs branch renormalization group flow. We find that this structure i…
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 formulate geometric conditions necessary for engineering 5d superconformal field theories (SCFTs) via M-theory compactification on a local Calabi-Yau 3-fold. Extending the classification of the rank 1 cases, which are realized geometrically as shrinking del Pezzo surfaces embedded in a 3-fold, we propose an exhaustive classification of local 3-folds engineering rank 2 SCFTs in 5d. This systematic classification confirms that all rank 2 SCFTs predicted using gauge theoretic arguments can be realized as consistent theories, with the exception of one family which is shown to be non-perturbativ…
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 the spectrum of BPS particles on the Coulomb branch of five-dimensional superconformal field theories (5d SCFTs) compactified on a circle. By engineering these theories in M-theory on ${\mathbf X} \times S^1 $, for ${\mathbf X}$ an isolated Calabi-Yau threefold singularity, we naturally identify the BPS category of the 5d theory on a circle with the derived category of coherent sheaves on a resolution of ${\mathbf X}$. It follows that the BPS spectrum can be studied in terms of 5d BPS quivers, which are the fractional-brane quivers for the singularity ${\mathbf X}$. 5d BPS quivers gen…
We extend the anomaly inflow methods developed in M-theory to SCFTs engineered via D3-branes in type IIB. We show that the 't Hooft anomalies of such SCFTs can be computed systematically from their geometric definition. Our procedure is tested in several 4d examples and applied to 2d theories obtained by wrapping D3-branes on a Riemann surface. In particular, we show how to analyze half-BPS regular punctures for 4d $\mathcal N = 4$ SYM on a Riemann surface. We discuss generalizations of this formalism to type IIB configurations with $F_3$, $H_3$ fluxes, as well as to F-theory setups.
This paper gives a classification of rank one 5d $\mathcal{N}=1$ and 6d $(1,0)$ SCFTs. The idea is to compactify 5d theory on $S^1$ and 6d theory on $T^2$ to get effective 4d $\mathcal{N}=2$ theory. These compactified theories all have a 4d $\mathcal{N}=2$ Coulomb branch whose solution can be described by mixed Hodge module (MHM). In the rank one case every Coulomb branch solution is related to rational elliptic surface with a section, whose classification is complete. So the classification is then reduced to pick up a subset from the data base of rational elliptic surface by imposing various …
Exact results are derived for 5d SCFTs with holographic duals in Type IIB supergravity. These theories have relevant deformations that flow to linear quiver gauge theories, with the number of nodes large in the large-$N$ limits described by supergravity. Starting from a suitable formulation of the matrix models resulting from supersymmetric localization of the squashed $S^5$ partition functions, the saddle point equations are solved for generic quivers with $N_f=2N$ at all interior nodes, which includes the $T_N$ theories, and for a sample of theories with $N_f\neq 2N$ nodes including theories…
We explore the \emph{Liouvillian} non-integrability criteria for long quiver gauge theories those preserve $ \mathcal{N}=1 $ SUSY in $ 5d $. We probe type IIB solutions with (an $ AdS_6 $ factor) semi-classical strings which capture the strong coupling dynamics of $ \mathcal{N}=1 $ SCFTs in $ 5d $. Our analysis reveals an underlying non-integrable structure within some sub-sector of these $ 5d $ SCFTs. To solidify our claim, we complement our analytic results through numerics. We estimate various chaos indicators for the phase space which confirm the onset of a \emph{chaotic} motion for these …
We revisit the correspondence between Calabi-Yau (CY) threefold isolated singularities $\mathbf{X}$ and five-dimensional superconformal field theories (SCFTs), which arise at low energy in M-theory on the space-time transverse to $\mathbf{X}$. Focussing on the case of toric CY singularities, we analyze the "gauge-theory phases" of the SCFT by exploiting fiberwise M-theory/type IIA duality. In this setup, the low-energy gauge group simply arises on stacks of coincident D6-branes wrapping 2-cycles in some ALE space of type $A_{M-1}$ fibered over a real line, and the map between the Kähler parame…
We propose a systematic approach to computing the BPS spectra of any 5d/6d supersymmetric quantum field theory in Coulomb phases, which admits either gauge theory descriptions or geometric descriptions, based on the Nakajima-Yoshioka's blowup equations. We provide a significant generalization of the blowup equation approach in terms of both properly quantized magnetic fluxes on the blowup $\hat{\mathbb{C}}^2$ and the effective prepotential for 5d/6d field theories on the Omega background which is uniquely determined by the Chern-Simons couplings on their Coulomb branches. We employ our method …
We study the central charges and levels of 2d $\mathcal{N}=(0,4)$ superconformal field theories that are dual to four- and five-dimensional BPS black holes in compactifications of type IIB string theory on a K3 surface. They arise from wrapping a D3-brane on a curve $C$ inside K3 and have transverse space either an ALE or ALF space. These D3-branes have an AdS$_3 \times \mathrm{S}^3/ Γ$ near horizon geometry where $Γ$ is a discrete subgroup of $SU(2)$. We compute the central charges and levels of the 2d SCFTs both in the microscopic picture and from six-dimensional $\mathcal{N}=(2,0)$ supergra…
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 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.
Little string theories (LSTs) are UV complete non-local 6D theories decoupled from gravity in which there is an intrinsic string scale. In this paper we present a systematic approach to the construction of supersymmetric LSTs via the geometric phases of F-theory. Our central result is that all LSTs with more than one tensor multiplet are obtained by a mild extension of 6D superconformal field theories (SCFTs) in which the theory is supplemented by an additional, non-dynamical tensor multiplet, analogous to adding an affine node to an ADE quiver, resulting in a negative semidefinite Dirac pairi…
We use holography to study codimension-2 surface defects in 5d SCFTs engineered by $(p,q)$ 5-brane webs. The three-dimensional defects are realized by D3-branes ending on the brane web. We identify the holographic representation of the defects in Type IIB $AdS_6$ solutions as probe D3-branes, and study conformal and non-conformal defects which, respectively, preserve one half and one quarter of the supersymmetry. For a sample of 5d SCFTs, including the $T_N$ theories, we provide explicit solutions for conformal and non-conformal defects. For the conformal defects we obtain their contribution t…
We study marginal deformations of a class of three-dimensional $\mathcal{N}=2$ SCFTs that admit a holographic dual description in massive type IIA supergravity. We compute the dimension of the conformal manifold in these SCFTs and identify a special submanifold with enhanced flavor symmetry. We show how to apply the TsT transformation of Lunin-Maldacena to construct explicit supersymmetric AdS$_4$ solutions of massive type IIA supergravity with non-trivial internal fluxes that are the holographic dual of these marginal deformations. Finally, we also briefly comment on a class of RG flows betwe…
We carry out a detailed exploration of the deformations of rank-two five-dimensional superconformal field theories (SCFTs) $\mathcal{T}_{\mathbf{X}}$, which are geometrically engineered by M-theory on the space transverse to isolated toric Calabi-Yau (CY) threefold singularities $\mathbf{X}$. Deformations of 5d $\mathcal{N}=1$ SCFTs can lead to "gauge-theory phases," but also to "non-gauge-theoretic phases," which have no known Lagrangian interpretation. In previous work, a technique relying on fiberwise M-theory/type IIA duality was developed to associate a type IIA background to any resoluti…
We probe type IIA geometries with \emph{folded} semiclassical strings those encode the strong coupling dynamics associated with long operators in a class of SCFTs pertaining to spacetimes whose dimension vary from $6d$ down to $2d$. We particularly focus on folded string configurations those are extended through stack of flavor $ Dp $ ($ p=6,8 $) branes localized along the internal manifold. Considering some specific examples within the realm of $ \mathcal{N}=2 $ linear quivers, we show that the associated string spectrum exhibits a pole as the string approaches flavor D6 branes. We identify t…
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 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 use recently established AdS$_6$/CFT$_5$ dualities to count the microstates of magnetically charged AdS$_6 \times S^2 \times Σ$ black holes in Type IIB. The near-horizon limit is described by solutions with AdS$_2 \times Σ_{\mathfrak{g}_1} \times Σ_{\mathfrak{g}_2} \times S^2 \times Σ$ geometry, where $Σ_{\mathfrak{g}_i}$ are Riemann surfaces of constant curvature and $Σ$ is a further Riemann surface over which the geometry is warped. Our results show that the topologically twisted indices of the proposed dual superconformal field theories precisely reproduce the Bekenstein-Hawking entropy …
We find an infinite family of $4D$ $\mathcal{N}=2$ interacting superconformal field theories which enter the description of the strong-coupling limit of $SU(2N+1)$ gauge theories with hypermultiplets in the $\wedge^2(\square)+\text{Sym}^2(\square)$ . These theories arise from the compactification of the $6D$ $(2,0)$ theory of type $A_{2N}$ on a sphere with two full twisted punctures and one minimal untwisted puncture. For $N=1$, this theory is the "new" rank-1 SCFT with $Δ(u)=3$ of Argyres and Wittig. Using the superconformal index, we finally pin down the properties of this theory.
We study six dimensional supergravity theories with superconformal sectors (SCFTs). Instances of such theories can be engineered using type IIB strings, or more generally F-Theory, which translates field theoretic constraints to geometry. Specifically, we study the fate of the discrete 2-form global symmetries of the SCFT sectors. For both $(2,0)$ and $(1,0)$ theories we show that whenever the charge lattice of the SCFT sectors is non-primitively embedded into the charge lattice of the supergravity theory, there is a subgroup of these 2-form symmetries that remains unbroken by BPS strings. By …
Starting from a general $\mathcal{N} = 2$ SCFT, we study the network of $\mathcal{N} = 1$ SCFTs obtained from relevant deformations by nilpotent mass parameters. We also study the case of flipper field deformations where the mass parameters are promoted to a chiral superfield, with nilpotent vev. Nilpotent elements of semi-simple algebras admit a partial ordering connected by a corresponding directed graph. We find strong evidence that the resulting fixed points are connected by a similar network of 4D RG flows. To illustrate these general concepts, we also present a full list of nilpotent def…
M5-branes probing an ADE singularity lead to 6D SCFTs with (1,0) supersymmetry. On the tensor branch, the M5-branes specify domain walls of a 7D Super Yang-Mills theory with gauge group G of ADE-type, thus providing conformal matter for a broad class of generalized quiver theories. Additionally, these theories have G x G flavor symmetry, and a corresponding Higgs branch. In this note we use the F-theory realization of these theories to calculate the scaling dimension of the operator parameterizing seven-brane recombination, i.e. motion of the stack of M5-branes off of the orbifold singularity.…
