We derive the corrections to the conformal dimensions of twisted Ramond ground states in the deformed two-dimensional $\mathcal N = (4,4)$ superconformal $(\mathbb T^4)^N/S_N$ orbifold theory describing bound states of the D1-D5 brane system in type IIB superstring theory. Our result holds to second order in the deformation parameter, and at the large $N$ planar limit. The method of calculation involves the analytic evaluation of integrals of four-point functions of two R-charged twisted Ramond fields and two marginal deformation operators. We also calculate the deviation from zero, at first order in the considered marginal perturbation, of the structure constant of the three-point function of two Ramond fields and one deformation operator.
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 …
Many three-dimensional $\mathcal{N}=2$ SCFTs admit a universal partial topological twist when placed on hyperbolic Riemann surfaces. We exploit this fact to derive a universal formula which relates the planar limit of the topologically twisted index of these SCFTs and their three-sphere partition function. We then utilize this to account for the entropy of a large class of supersymmetric asymptotically AdS$_4$ magnetically charged black holes in M-theory and massive type IIA string theory. In this context we also discuss novel AdS$_2$ solutions of eleven-dimensional supergravity which describe…
We compute spin $ 2 $ spectrum associated with massive graviton fluctuations in $γ$-deformed Gaiotto-Maldacena background those are holographically dual to marginal deformations of $\mathcal{N}=2$ SCFTs in four dimensions. Under the special circumstances, we analytically estimate the spectra both for the $ γ$- deformed Abelian T dual (ATD) as well as the non-Abelian T dual (NATD) cases where we retain ourselves upto leading order in the deformation parameter. Our analysis reveals a continuous spectra which is associated with the breaking of the $ U(1) $ isometry (along the directions of the in…
We study various aspects of the mass deformed SYK model which can escape the interiors of pure boundary state black holes. SYK boundary states are given by a simple local boundary condition on the Majorana fermions and then evolved in Euclidean time in the SYK Hamiltonian. We study the ground state of this mass deformed SYK model in detail. We also use SYK boundary states as a variational approximation to the ground state of the mass deformed SYK model. We compare variational approximation with the exact ground state results and they showed a good agreement. We also study the time evolution of…
We study two families of composite twisted Ramond fields (made by products of two operators) in the $\cal {N}=(4,4)$ supersymmetric D1-D5 SCFT$_2$ deformed by a marginal modulus operator away from its $(T^4)^N/ S_N$ free orbifold point. We construct the large-$N$ contributions to the four-point functions with two composite operators and two deformation fields. These functions allow us to derive short-distance OPE limits and to calculate the anomalous dimensions of the composite operators. We demonstrate that one can distinguish two sets of composite Ramond states with twists $m_1$ and $m_2$: p…
We determine the one-loop deformation of the conformal symmetry of a general N}=2 superconformally invariant Yang-Mills theory. The deformation is computed for several explicit examples which have a realization as world-volume theories on a stack of D3 branes. These include (i) N=4 SYM with gauge groups SU(N), USp(2N) and SO(N); (ii) USp(2N) gauge theory with one hypermultiplet in the traceless antisymmetric representation and four hypermultiplets in the fundamental; (iii) quiver gauge theory with gauge group SU(N)xSU(N) and two hypermultiplets in the bifundamental representations (N,\bar N) a…
We find a class of new supersymmetric dyonic black holes in four-dimensional maximal gauged supergravity which are asymptotic to the ${\rm SU(3)}\times {\rm U(1)}$ invariant AdS$_4$ Warner vacuum. These black holes can be embedded in eleven-dimensional supergravity where they describe the backreaction of M2-branes wrapped on a Riemann surface. The holographic dual description of these supergravity backgrounds is given by a partial topological twist on a Riemann surface of a three-dimensional $\mathcal{N}=2$ SCFT that is obtained by a mass-deformation of the ABJM theory. We compute explicitly t…
The Higgs branch of the D1D5 system flows in the infrared to a two-dimensional N=(4,4) SCFT. This system is believed to have an "orbifold point" in its moduli space where the SCFT is a free sigma model with target space the symmetric product of copies of four-tori; however, at the orbifold point gravity is strongly coupled and to reach the supergravity point one needs to turn on the four exactly marginal deformations corresponding to the blow-up modes of the orbifold SCFT. Recently, technology has been developed for studying these deformations and perturbing the D1D5 CFT off its orbifold point…
We calculate the $\mathcal{S}$-multiplets for two-dimensional Euclidean $\mathcal{N}=(0,2)$ and $\mathcal{N} = (2,2)$ superconformal field theories under the $T\overline{T}$ deformation at leading order of perturbation theory in the deformation coupling. Then, from these $\mathcal{N} = (0, 2)$ deformed multiplets, we calculate two- and three-point correlators. We show the $\mathcal{N} = (0,2)$ chiral ring's elements do not flow under the $T\overline{T}$ deformation. Specializing to integrable supersymmetric seed theories, such as $\mathcal{N} = (2,2)$ Landau-Ginzburg models, we use the thermod…
We study D3-brane theories that are dually described as deformations of two different $\mathcal{N}=2$ superconformal theories with massless monopoles and dyons. These arise at the self-intersection of a seven-brane in F-theory, which cuts out a link on a small three-sphere surrounding the self-intersection. The spectrum is studied by taking small loops in the three-sphere, yielding a link-induced monodromy action on string junction D3-brane states, and subsequently quotienting by the monodromy. This reduces the differing flavor algebras of the $\mathcal{N}=2$ theories to the same flavor algebr…
We consider a class of pure black hole microstates and demonstrate that they can be made escapable by turning on certain double trace deformations in the CFT. These microstates are dual to BCFT states prepared via a Euclidean path integral starting from a boundary in Euclidean time. These states are dual to black holes in the bulk with an End-of-the-World brane; a codimension one timelike boundary of the spacetime behind the horizon. We show that by tuning the sign of the coupling of the double trace operator to the boundary conditions on the brane the deformation injects negative energy into …
It has recently been conjectured that the closed topological string wave function computes a grand canonical partition function of BPS black hole states in 4 dimensions: Z_BH=|psi_top|^2. We conjecture that the open topological string wave function also computes a grand canonical partition function, which sums over black holes bound to BPS excitations on D-branes wrapping cycles of the internal Calabi-Yau: Z^open_BPS=|psi^open_top|^2. This conjecture is verified in the case of Type IIA on a local Calabi-Yau threefold involving a Riemann surface, where the degeneracies of BPS states can be comp…
We construct the wave functions in the q-deformed 2d Yang-Mills theory that compute torus correlation functions of affine currents in the VOA associated to a class of 4d $N = 2$ SCFTs. These wave functions are then shown to reduce to the topological correlators of a set of Coulomb branch operators in the $T[SU(N)]$ theory, from which those correlators in the 3d mirror dual of the 4d TN theories can be computed.
We obtain microstates accounting for the Gibbons-Hawking entropy in $dS_3$, along with a subleading logarithmic correction, from the solvable $T\bar T+Λ_2$ deformation of a seed CFT with sparse light spectrum. The microstates arise as the dressed CFT states near dimension $Δ=c/6$, associated with the Hawking-Page transition; they dominate the real spectrum of the deformed theory. We exhibit an analogue of the Hawking-Page transition in de Sitter. Appropriate generalizations of the $T\bar T+Λ_2$ deformation are required to treat model-dependent local bulk physics (subleading at large central ch…
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 explore the Ramond sector of the deformed two-dimensional $\cal N = (4, 4)$ superconformal $(T^4)^N /S_N$ orbifold theory, describing bound states of D1-D5 brane system in type IIB superstring. We derive the large-$N$ limit of the four-point function of two R-charged twisted Ramond fields and two marginal deformation operators at the free orbifold point. Specific short-distance limits of this function provide several structure constants, the OPE fusion rules and the conformal dimensions of a few non-BPS operators. The second order correction (in the deformation parameter) to the two-point f…
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…
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 discuss in detail the different analogues of Dolbeault cohomology groups on Sasaki-Einstein manifolds and prove a new vanishing result for the transverse Dolbeault cohomology groups $H_{\bar\partial}^{(p,0)}(k)$ graded by their charge under the Reeb vector. We then introduce a new cohomology, $η$-cohomology, which is defined by a CR structure and a holomorphic function $f$ with non-vanishing $η\equiv \mathrm{d}f$. It is the natural cohomology associated to a class of supersymmetric type IIB flux backgrounds that generalise the notion of a Sasaki-Einstein manifold. These geometries are dual …
In this paper we propose the identification in AdS4 N = 2 gauged supergravity of the coefficient $τ_{RR}$ of 3D N = 2 SCFTs. We constraint the structure of this function in supergravity by combining the results from unitarity, holography and localization. We show that our conjectured function is minimized by the exact R-charge, corresponding to a gravitational attractor for the scalars in the special geometry. We identify this mechanism with the supergravity dual of the $τ_{RR}$-minimization. We check this proposal in the ABJM model, comparing with the expectations from localization and the Ad…
We study the relationship between instanton counting in N=4 Yang-Mills theory on a generic four-dimensional toric orbifold and the semi-classical expansion of q-deformed Yang-Mills theory on the blowups of the minimal resolution of the orbifold singularity, with an eye to clarifying the recent proposal of using two-dimensional gauge theories to count microstates of black holes in four dimensions. We describe explicitly the instanton contributions to the counting of D-brane bound states which are captured by the two-dimensional gauge theory. We derive an intimate relationship between the two-di…
It is shown how the deformation of the superconformal generators on the string's worldsheet by a nonabelian super-Wilson line gives rise to a covariant exterior derivative on loop space coming from a nonabelian 2-form on target space. The expression obtained this way is new in the context of strings, and its consistency is verified by checking that its global gauge transformations on loop space imply the familiar gauge transformations on target space. We derive the second order gauge transformation from infinitesimal local gauge transformations on loop space and find that a consistent picture …
We generalize, in a manifestly Weyl-invariant way, our previous expressions for irregular singularity wave functions in two-dimensional SU(2) q-deformed Yang-Mills theory to SU(N). As an application, we give closed-form expressions for the Schur indices of all (A_{N-1}, A_{N(n-1)-1}) Argyres-Douglas (AD) superconformal field theories (SCFTs), thus completing the computation of these quantities for the (A_N, A_M) SCFTs. With minimal effort, our wave functions also give new Schur indices of various infinite sets of "Type IV" AD theories. We explore the discrete symmetries of these indices and al…
We describe the effect of the marginal deformation of the $\cal N = (4, 4)$ superconformal $(T^4)^N /S_N$ orbifold theory on a doublet of R-neutral twisted Ramond fields, in the large-$N$ approximation. Our analysis of their dynamics explores the explicit analytic form of the genus-zero four-point function involving two R-neutral Ramond fields and two deformation operators. We compute this correlation function with two different approaches: the Lunin-Mathur path-integral technique and the stress-tensor method. From its short distance limits, we extract the OPE structure constants and the scali…
We conjecture a closed-form expression for the Schur limit of the superconformal index of two infinite series of Argyres-Douglas (AD) superconformal field theories (SCFTs): the (A_1,A_{2n-3}) and the (A_1,D_{2n}) theories. While these SCFTs can be realized at special points on the Coulomb branch of certain N=2 gauge theories, their superconformal R symmetries are emergent, and hence their indices cannot be evaluated by localization. Instead, we construct the (A_1, A_{2n-3}) and (A_1, D_{2n}) indices by using a relation to two-dimensional q-deformed Yang-Mills theory and data from the class S c…
We study the free energy of four-dimensional CFTs on deformed spheres. For generic nonsupersymmetric CFTs only the coefficient of the logarithmic divergence in the free energy is physical, which is an extremum for the round sphere. We then specialize to $\mathcal{N}=2$ SCFTs where one can preserve some supersymmetry on a compact manifold by turning on appropriate background fields. For deformations of the round sphere the $c$ anomaly receives corrections proportional to the supersymmetric completion of the (Weyl)$^2$ term, which we determine up to one constant by analyzing the scale dependence…
In this article we use 5-brane junctions to study the 5D T_N SCFTs corresponding to the 5D N=1 uplift of the 4D N=2 strongly coupled gauge theories, which are obtained by compactifying N M5 branes on a sphere with three full punctures. Even though these theories have no Lagrangian description, by using the 5-brane junctions proposed by Benini, Benvenuti and Tachikawa, we are able to derive their Seiberg-Witten curves and Nekrasov partition functions. We cross-check our results with the 5D superconformal index proposed by Kim, Kim and Lee. Through the AGTW correspondence, we discuss the relatio…
Recent years have witnessed lots of progress in the computation of supersymmetric partition functions of SCFTs on curved manifolds via localization. The twisted partition function on product manifolds of the form $S^1 \times Σ_g$, where $Σ_g$ is a two-dimensional Riemann surface, is of particular relevance due to its role in the microstate counting for magnetic static AdS$_4$ black holes realizing the topological twist. We review here supergravity solutions having as conformal boundary more general 3d manifolds. We first focus on solutions (AdS-Taub-NUT and AdS-Taub-Bolt) having as boundary a …
We generate new AdS_4 solutions of D=11 supergravity starting from AdS_4 x X_7 solutions where X_7 has U(1)^3 isometry. We consider examples where X_7 is weak G_2, Sasaki-Einstein or tri-Sasakian, corresponding to d=3 SCFTs with N=1,2 or 3 supersymmetry, respectively, and where the deformed solutions preserve N=1,2 or 1 supersymmetry, respectively. For the special cases when X_7 is M(3,2), Q(1,1,1) or N(1,1)_I we identify the exactly marginal deformation in the dual field theory. We also show that the volume of supersymmetric 5-cycles of N(1,1)_I agrees with the conformal dimension predicted b…
The free orbifold point of the D1-D5 CFT must be deformed with a scalar marginal operator driving it to the region in moduli space where the holographic supergravity description of fuzzball microstates becomes available. We discuss the effects of the deformation operator on the twisted Ramond ground states of the CFT by computing four-point functions. One can thus extract the OPEs of the deformation operator with these Ramond fields to find the conformal dimensions of intermediate non-BPS states and the relevant structure constants. We also compute the anomalous dimensions at second order in p…
We construct the one-dimensional topological sector of $\mathcal N = 6$ ABJ(M) theory and study its relation with the mass-deformed partition function on $S^3$. Supersymmetric localization provides an exact representation of this partition function as a matrix integral, which interpolates between weak and strong coupling regimes. It has been proposed that correlation functions of dimension-one topological operators should be computed through suitable derivatives with respect to the masses, but a precise proof is still lacking. We present non-trivial evidence for this relation by computing the …
In this article we explore the duality between the low energy effective theory of five-dimensional N=1 SU(N)^{M-1} and SU(M)^{N-1} linear quiver gauge theories compactified on S^1. The theories we study are the five-dimensional uplifts of four-dimensional superconformal linear quivers. We study this duality by comparing the Seiberg-Witten curves and the Nekrasov partition functions of the two dual theories. The Seiberg-Witten curves are obtained by minimizing the worldvolume of an M5-brane with nontrivial geometry. Nekrasov partition functions are computed using topological string theory. The …
Supersymmetry allows a $D^4 R^4$ interaction in M-theory, but such an interaction is inconsistent with string theory dualities and so is known to be absent. We provide a novel proof of the absence of the $D^4 R^4$ M-theory interaction by calculating 4-point scattering amplitudes of 11d supergravitons from ABJM theory. This calculation extends a previous calculation performed to the order corresponding to the $R^4$ interaction. The new ingredient in this extension is the interpretation of the fourth derivative of the mass deformed $S^3$ partition function of ABJM theory, which can be determined…
We study $\mathcal{N}=2$ theories on four-dimensional manifolds that admit a Killing vector $v$ with isolated fixed points. It is possible to deform these theories by coupling position-dependent background fields to the flavor current multiplet. The partition function of the deformed theory only depends on the value of the background scalar fields at the fixed points of $v$. For a single adjoint hypermultiplet, the partition function becomes independent of the supergravity as well as the flavor background if the scalars attain special values at the fixed points. For these special values, super…
