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.
We study entanglement entropy and the free energy in recently constructed holographic duals for 5d SCFTs in type IIB supergravity. The solutions exhibit mild singularities, which could potentially complicate holographic applications. We use the relation of the entanglement entropy for a spherical entangling surface to the free energy of the field theory on the five sphere as a well-motivated benchmark to assess how problematic the singularities are. The holographic supergravity computations give well-defined results for both quantities and they satisfy the expected relations. This supports the…
We present a systematic search for Type IIB supergravity solutions whose spacetimes include AdS5 and S2 factors, which would be candidate duals to N = 2 four-dimensional Superconformal field theories. The candidate solutions encode the SU(2) R-symmetry geometrically on the S2 and an additional Killing vector generates the U(1) R-symmetry. By analysing the Killing spinor equations we show that no such solutions exist. This suggests that, if Type IIB backgrounds dual to N = 2 SCFTs exist, the SU(2) R-symmetry is realised non-geometrically. Finally, we also show that, in the context of both N = 1…
We derive the full Kaluza-Klein spectrum of type IIB supergravity compactified on AdS_5 x T^{11} with T^{11} = (SU(2) x SU(2))/U(1). From the knowledge of the spectrum and general multiplet shortening conditions, we make a refined test of the AdS/CFT correspondence, by comparison between various shortenings of SU(2,2|1) supermultiplets on AdS_5 and different families of boundary operators with protected dimensions. Additional towers of long multiplets with rational dimensions, that are not protected by supersymmetry, are also predicted from the supergravity analysis.
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 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 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 study the 't Hooft anomalies of four-dimensional superconformal field theories that arise from M5-branes wrapped on a punctured Riemann surface. In general there are two independent contributions to the anomalies. There is a bulk term obtained by integrating the anomaly polynomial of the world-volume theory on the M5-branes over the Riemann surface; this contribution knows about the punctures only through its dependence on the Euler characteristic of the surface. The second set of contributions comes from local data at the punctures; these terms are independent from the bulk data of the sur…
We construct Type IIB supergravity solutions with geometry $AdS_6\times S^2$ warped over a disc with two boundary points where 5-branes emerge and punctures with 7-brane monodromy. They describe $(p,q)$ 5-brane junctions with two groups of like-charged external 5-branes that are unconstrained by the $s$-rule and an additional group of constrained 5-branes. The dual 5d SCFTs include various theories discussed previously in the literature. We match SCFT operators with scaling dimension of $\mathcal O(N)$ with their representation in supergravity to support the proposed dualities.
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…
It is known that a 4d N = 1 SCFT lives on D3-branes probing a local del Pezzo Calabi-Yau singularity. The Seiberg (or toric) duality of this SCFT arises from the Picard-Lefshetz transformation of the affine E_N 7-brane background that is associated with the Calabi-Yau threefold. In this paper we study the duality of the affine E_N background itself and a 5-brane probing it. We then find that many different Type IIB 5-brane webs describe the same SCFT in 5d. We check this duality by comparing the Nekrasov partition functions of these 5-brane web configurations.
We describe a method to determine the anomaly polynomials of general 6d $\mathcal{N}=(2,0)$ and $\mathcal{N}=(1,0)$ SCFTs, in terms of the anomaly matching on their tensor branches. This method is almost purely field theoretical, and can be applied to all known 6d SCFTs. We demonstrate our method in many concrete examples, including $\mathcal{N}=(2,0)$ theories of arbitrary type and the theories on M5 branes on ALE singularities, reproducing the $N^3$ behavior. We check the results against the anomaly polynomials computed M-theoretically via the anomaly inflow.
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 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…
Higgs Branch and VOA of 4d $\mathcal{N}=2$ SCFTs from IIB
School of Physics, Peking University（北京大学物理学院）；Center for High Energy Physics, Peking University（北京大学高能物理中心）；Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）
We provide further evidence that the recently constructed warped $AdS_6$ solutions in Type IIB supergravity are dual to 5d SCFTs that correspond to $(p,q)$ 5-brane webs with large numbers of like-charged external 5-branes. We study a number of specific examples, including the $T_N$ theory, and identify the bulk states dual to a class of operators with ${\cal O}(N)$ scaling dimensions in terms of strings and string-webs embedded in the solutions.
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 study solutions of type IIB string theory dual to ${\cal N}=4$ supersymmetric Yang-Mills theory on half of $\mathbb{R}^{3,1}$ coupled to holographic three-dimensional superconformal field theories (SCFTs) at the edge of this half-space. The dual geometries are asymptotically $AdS^5 \times S^5$ with boundary geometry $\mathbb{R}^{2,1} \times \mathbb{R}^+$, with a geometrical end-of-the-world (ETW) brane cutting off the other half of the asymptotic region of the would-be Poincaré $AdS^5 \times S^5$. We show that by choosing the 3D SCFT appropriately, this ETW brane can be pushed arbitrarily f…
We use the formalism of generalized geometry to study the generic supersymmetric AdS_5 solutions of type IIB supergravity that are dual to N=1 superconformal field theories (SCFTs) in d=4. Such solutions have an associated six-dimensional generalized complex cone geometry that is an extension of Calabi-Yau cone geometry. We identify generalized vector fields dual to the dilatation and R-symmetry of the dual SCFT and show that they are generalized holomorphic on the cone. We carry out a generalized reduction of the cone to a transverse four-dimensional space and show that this is also a general…
We apply c-extremization, whose proof we review in full detail, to study two-dimensional N=(0,2) superconformal field theories arising from the low-energy dynamics of D3-branes wrapped on Riemann surfaces and M5-branes wrapped on four-manifolds. We compute the exact central charges of these theories using anomalies and c-extremization. In all cases we also construct AdS_3 supergravity solutions of type IIB and eleven-dimensional supergravity, which are holographic duals to the field theories at large N, and exactly reproduce the central charges computed via c-extremization.
We analyze topological mass terms of BF type arising in supersymmetric M-theory compactifications to $AdS_5$. These describe spontaneously broken higher-form gauge symmetries in the bulk. Different choices of boundary conditions for the BF terms yield dual field theories with distinct global discrete symmetries. We discuss in detail these symmetries and their 't Hooft anomalies for 4d $\mathcal N = 1$ SCFTs arising from M5-branes wrapped on a Riemann surface without punctures, including theories from M5-branes at a $\mathbb Z_2$ orbifold singularity. The anomaly polynomial is computed via infl…
We derive the anomaly polynomials of 4d $\mathcal{N}=2$ theories that are obtained by wrapping M5-branes on a Riemann surface with arbitrary regular punctures, using anomaly inflow in the corresponding M-theory setup. Our results match the known anomaly polynomials for the 4d $\mathcal{N}=2$ class $\mathcal{S}$ SCFTs. In our approach, the contributions to the 't Hooft anomalies due to boundary conditions at the punctures are determined entirely by $G_4$-flux in the 11d geometry. This computation provides a top-down derivation of these contributions that utilizes the geometric definition of the…
We present new classes of explicit supersymmetric AdS_3 solutions of type IIB supergravity with non-vanishing five-form flux and AdS_2 solutions of D=11 supergravity with electric four-form flux. The former are dual to two-dimensional SCFTs with (0,2) supersymmetry and the latter to supersymmetric quantum mechanics with two supercharges. We also investigate more general classes of AdS_3 solutions of type IIB supergravity and AdS_2 solutions of D=11 supergravity which in addition have non-vanishing three-form flux and magnetic four-form flux, respectively. The construction of these more general…
We consider Type IIB 5-brane configurations for 5d rank 2 superconformal theories which are classified recently by geometry in arXiv:1801.04036. We propose all the 5-brane web diagrams for these rank 2 theories and show dualities between some of different gauge theories with explicit duality map of mass parameters and Coulomb branch moduli. In particular, we explicitly construct 5-brane configurations for $G_2$ gauge theory with six flavors and its dual $Sp(2)$ and $SU(3)$ gauge theories. We also present 5-brane webs for $SU(3)$ theories of Chern-Simons level greater than 5.
Five- and four-dimensional superconformal field theories with eight supercharges arise from canonical threefold singularities in M-theory and Type IIB string theory, respectively. We study their Coulomb and Higgs branches using crepant resolutions and deformations of the singularities. We propose a relation between the resulting moduli spaces, by compactifying the theories to 3d, followed by 3d $\mathcal{N}=4$ mirror symmetry and an $S$-type gauging of an abelian flavor symmetry. In particular, we use this correspondence to determine the Higgs branch of some 5d SCFTs and their magnetic quivers…
We present evidence that for each ADE Lie group G there is an infinite tower of 4D N=2 SCFTs, which we label as D(G,s) (with s a positive integer), having (at least) flavor symmetry G. For G=SU(2), D(SU(2),s) coincides with the Argyres--Douglas model of type D_{s+1}, while for larger flavor groups the models are new (but for a few previously known examples). When its flavor symmetry G is gauged, D(G,s) contributes to the Yang-Mills beta-function as s/[2(s+1)] adjoint hypermultiplets. The argument is based on a combination of Type IIB geometric engineering and the categorical deconstruction of …
In this paper a Penrose limit is constructed for type IIB $AdS_6\times S^2\times Σ$ supergravity solutions. These solutions are dual to five dimensional SCFTs related to (p,q) five brane webs, which can often be described in terms of long quiver gauge theories. The null geodesic from which the Penrose limit is constructed is localized at a unique point on the two dimensional Riemann surface $Σ$, where the $AdS_6$ and $S^2$ metric factors are extremal. The resulting pp-wave spacetime takes a universal form. The world sheet action of the Green-Schwarz string is quadratic in the light cone gauge …
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…
Variants of the black hole information paradox are studied in Type IIB string theory setups that realize four-dimensional gravity coupled to a bath. The setups are string theory versions of doubly-holographic Karch/Randall brane worlds, with black holes coupled to non-gravitating and gravitating baths. The 10d versions are based on fully backreacted solutions for configurations of D3, D5 and NS5 branes, and admit dual descriptions as $\mathcal N=4$ SYM on a half space and 3d $T_ρ^σ[SU(N)]$ SCFTs. Island contributions to the entanglement entropy of black hole radiation systems are identified th…
We report on tests of the AdS/CFT correspondence that are made possible by complete knowledge of the Kaluza-Klein mass spectrum of type IIB supergravity on $AdS_5 \times T^{11}$ with T^{11}=SU(2)^2/U(1). After briefly discussing general multiplet shortening conditions in SU(2,2|1) and PSU(2,2|4), we compare various types of short SU(2,2|1) supermultiplets on AdS_5 and different families of boundary operators with protected dimensions. The supergravity analysis predicts the occurrence in the SCFT at leading order in N and g_s N, of extra towers of long multiplets whose dimensions are rational b…
We construct new families of $\text{AdS}_2 \times S^2 \times S^2$ solutions with 4 supercharges in Type II supergravities. We show that subclasses of these solutions can be interpreted in terms of defect branes embedded in 4d $\mathcal{N} = 4 $ SYM, or orbifolds thereof. This is explicitly realised by showing that the solutions asymptote locally to $\text{AdS}_5 \times S^5/\mathbb{Z}_n$, in Type IIB, or its T-dual background, in Type IIA. The latter is a Gaiotto-Maldacena geometry realised on an intersection of D4 and NS5 branes. We extend the Type IIA solutions to include D6 branes, and inter…
We give full details for the computation of the Kaluza--Klein mass spectrum of Type IIB Supergravity on AdS_5 x T^{11}, with T^{11}=SU(2)xSU(2)/U(1), that has recently lead to both stringent tests and interesting predictions on the AdS_5/CFT_4 correspondence for N=1 SCFT's (hep-th/9905226). We exhaustively explain how KK states arrange into SU(2,2|1) supermultiplets, and stress some relevant features of the T^{11} manifold, such as the presence of topological modes in the spectrum originating from the existence of non-trivial 3-cycles. The corresponding Betti vector multiplet is responsible fo…
We study Type IIB supergravity solutions with spacetime of the form $AdS_6\times S^2$ warped over a Riemann surface $Σ$, where $Σ$ includes punctures around which the supergravity fields have non-trivial $SL(2,R)$ monodromy. Solutions without monodromy have a compelling interpretation as near-horizon limits of $(p,q)$ 5-brane webs, and the punctures have been interpreted as additional 7-branes in the web. In this work we provide further support for this interpretation and clarify several aspects of the identification of the supergravity solutions with brane webs. To further support the identif…
We consider the 6d (1,0) SCFT on a stack of $N$ M5-branes probing a $\mathbb C^2/\mathbb Z_2$ singularity. In particular, we study its compactifications to four dimensions on a smooth genus-$g$ Riemann surface with non-trivial flavor flux, yielding a family of 4d CFTs. By tracking the M-theory origin of the global symmetries of the 4d CFTs, we detect the emergence of an accidental symmetry and the spontaneous symmetry breaking of a $U(1)$ generator. These effects are visible from geometric considerations and not apparent from the point of view of the compactification of the 6d field theory. Th…
We develop the notion of double holography in Type IIB string theory realizations of braneworld models. The Type IIB setups are based on the holographic duals of 4d BCFTs comprising 4d $\mathcal N=4$ SYM on a half space coupled to 3d $\mathcal N=4$ SCFTs on the boundary. Based on the concrete BCFTs and their brane construction, we provide microscopic realizations of the intermediate holographic description, obtained by dualizing only the 3d degrees of freedom. Triggered by recent observations in bottom-up models, we discuss the causal structures in the full BCFT duals and intermediate descript…
We report on the computation of the one-instanton contribution to the 16-point Green function of fermionic composite operators in N=4 Super YM theory. The remarkable agreement, initially found in the case of an SU(2) gauge group, with the one D-instanton contribution to the corresponding type IIB superstring amplitude on $AdS_5\times S^5$ is reviewed here. The recent extension by other authors of this result to any SU(N) gauge group and to multi-instantons in the large N limit is briefly discussed. We also argue that for the AdS/SCFT correspondence under consideration to work for any $N\geq 2$…
We construct infinite new classes of $AdS_4\times S^1\times S^5$ solutions of type IIB string theory which have non-trivial $SL(2,\mathbb{Z})$ monodromy along the $S^1$ direction. The solutions are supersymmetric and holographically dual, generically, to $\mathcal{N}=1$ SCFTs in $d=3$. The solutions are first constructed as $AdS_4\times \mathbb{R}$ solutions in $D=5$ $SO(6)$ gauged supergravity and then uplifted to $D=10$. Unlike the known $AdS_4\times \mathbb{R}$ S-fold solutions, there is no continuous symmetry associated with the $\mathbb{R}$ direction. The solutions all arise as limiting c…
AdS_3 solutions dual to N = (0,2) SCFTs arise when D3-branes wrap Kahler two-cycles in manifolds with SU(4) holonomy. Here we review known AdS_3 solutions and identify the corresponding three-dimensional gauged supergravities, solutions of which uplift to type IIB supergravity. In particular, we discuss gauged supergravities dual to twisted compactifications on Riemann surfaces of both N=4 SYM and N =1 SCFTs with Sasaki-Einstein duals. We check in each case that c-extremization gives the exact central charge and R symmetry. For completeness, we also study AdS_3 solutions from intersecting D3-b…
In this thesis we give a pedagogical introduction to the construction of NS5-D6(-O6)-D8(-O8) brane setups in massive type IIA string theory and the six-dimensional $(1,0)$ SCFT's they engineer. After describing how to introduce the various ingredients (and their interplay) in type IIA, we explain how to read off an effective linear quiver description of the SCFT's from the brane setups. We then explain in detail how to construct all AdS$_7$ solutions of massive IIA supergravity which are dual to the field theories. We do this by exploiting the power of generalized complex geometry. We then sho…
We propose 5d descriptions of 6d ${\cal N}=(1,0)$ superconformal field theories arising from Type IIA brane configurations with an $O8^-$-plane. We T-dualize the brane diagram along a compactification circle and obtain a 5-brane web diagram with two $O7^-$-planes. The gauge theory description of the resulting 5d theory for a given 6d superconformal field theory is not unique, and we argue that the non-uniqueness leads to various dual 5d gauge theories. There are three sources which lead to the 5d dualities. One type comes from either resolving both or one of the two $O7^-$-planes. The two situ…
We consider bound states of strings which arise in 6d (1,0) SCFTs that are realized in F-theory in terms of linear chains of spheres with negative self-intersections 1,2, and 4. These include the strings associated to N small E8 instantons, as well as the ones associated to M5 branes probing A and D type singularities in M-theory or D5 branes probing ADE singularities in Type IIB string theory. We find that these bound states of strings admit (0,4) supersymmetric quiver descriptions and show how one can compute their elliptic genera.
We consider 4d field theories obtained by reducing the 6d (1,0) SCFT of $N$ M5-branes probing a $\mathbb C^2/\mathbb Z_k$ singularity on a Riemann surface with fluxes. We follow two different routes. On the one hand, we consider the integration of the anomaly polynomial of the parent 6d SCFT on the Riemann surface. On the other hand, we perform an anomaly inflow analysis directly from eleven dimensions, from a setup with M5-branes probing a resolved $\mathbb C^2/\mathbb Z_k$ singularity fibered over the Riemann surface. By comparing the 4d anomaly polynomials, we provide a characterization of …
Type IIB AdS$_6$ solutions with orientifold 7-planes are constructed. The geometry is a warped product of AdS$_6$ and S$^2$ over a Riemann surface $Σ$ and the O7-planes correspond to a particular type of puncture on $Σ$. The solutions are identified as near-horizon limits of $(p,q)$ 5-brane webs with O7-planes. The dual 5d SCFTs have relevant deformations to linear quiver gauge theories which have $SO(\cdot)$ or $USp(\cdot)$ nodes or $SU(\cdot)$ nodes with hypermultiplets in symmetric or antisymmetric representations, in addition to $SU(\cdot)$ nodes with fundamental hypermultiplets. The S$^5$…
We consider the circle and torus compactification of a certain subclass of 6d $\mathcal{N}=(1,0)$ SCFTs which are Higgsable to the higher rank E-string theories. Using the T-duality between Type I' and Type IIB, we found that the $S^1$ compactification of the theories can be realized by 5-brane webs describing the 5d uplifting of a specified class S theory, generalizing the result by Benini, Benvenuti and Tachikawa. We checked the above result by calculating conformal and flavor central charges of the 4d torus compactified theory both from the tensor branch structure of the 6d theory and from …
