A massive deformation of the T[SU(N)] theory is identified as the 3d SCFT realizing the RG-wall and half-BPS boundaries in 4d N=2 SU(N) SYM.
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An Index for 4 dimensional Super Conformal Theories
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We present a trace formula for an index over the spectrum of four dimensional superconformal field theories on $S^3 \times $ time. Our index receives contributions from states invariant under at least one supercharge and captures all information -- that may be obtained purely from group theory -- about protected short representations in 4 dimensional superconformal field theories. In the case of the $\mathcal{N}=4$ theory our index is a function of four continuous variables. We compute it at weak coupling using gauge theory and at strong coupling by summing over the spectrum of free massless particles in $AdS_5\times S^5$ and find perfect agreement at large $N$ and small charges. Our index does not reproduce the entropy of supersymmetric black holes in $AdS_5$, but this is not a contradiction, as it differs qualitatively from the partition function over supersymmetric states of the ${\cal N}=4$ theory. We note that entropy for some small supersymmetric $AdS_5$ black holes may be reproduced via a D-brane counting involving giant gravitons. For big black holes we find a qualitative (but not exact) agreement with the naive counting of BPS states in the free Yang Mills theory. In this paper we also evaluate and study the partition function over the chiral ring in the $\mathcal{N}=4$ Yang Mills theory.
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hep-th 21representative citing papers
Enumerates 244 fortuitous operators in ABJM theory and identifies a truncation matching the BMN subsector of N=4 SYM to lift an infinite tower of representatives.
Generalized Schur partition functions Z_USp(2N)(q; alpha) for 4d N=2 USp(2N) theories satisfy order-(N+1) MLDEs with vanishing Wronskian index, alpha fixing MLDE parameters, with links to RCFT characters and a conjecture on quantum monodromy traces.
Constructs fermionic extensions of W-algebras W^{-N+1}(sl_N, f_sub) via BRST cohomology in 3d N=4 abelian gauge theories and explicitly computes the N=3 case as an extension of the Bershadsky-Polyakov algebra.
The supersymmetric index in a one-fermion matrix model for N=4 SYM is independent of N due to exact cancellations between bosonic and fermionic trace relations.
Berry curvature of BPS states is random-matrix-like for supersymmetric black hole microstates but non-random and often zero for horizonless geometries, offering a chaos diagnostic in degenerate sectors.
A refined 3D index is defined by adding flavor symmetry gradings to the superconformal index of T[M], yielding an explicit infinite-sum formula from Dehn surgery that is claimed to be a strictly stronger invariant than the standard 3D index.
Unitary matrix models are mapped to vacuum correlators of quantized symmetric functions in the N-magnon sector of a spin chain via Schur orthogonality.
The |G|-fold degeneracy of supersymmetric AdS5 black hole index saddles is fixed by the flux-quantized BF coupling of the bulk one-form symmetry and persists unmodified in the decompactified black-brane limit.
Constructs complex BTZ x S3 saddles for the supersymmetric index in AdS3 x S3 supergravity, matching supersymmetry requirements through two-center 4D solutions with complex charges and 6D black strings.
A non-Lorentzian scalar QFT with SU(1,1) symmetry obtained from N=4 SYM is finite at all orders in perturbation theory.
Proposes complex matrix models for BPS correlators in N=4 SYM, relating eigenvalue distributions to LLM droplet shapes and enabling computations of one-point functions and three-point correlators via reductions to known models.
High-temperature limits on higher sheets of the superconformal index for (A1,A2n) Argyres-Douglas theories yield Gang-Kim-Stubbs 3d N=2 theories whose boundaries support Virasoro minimal model VOAs M(2,2n+3) and associated MTCs.
Exact quarter-indices for basic ortho-symplectic corners in N=4 SYM are obtained in closed form, proven equal under duality, and interpreted as vacuum characters of BCD W-algebras and osp(1|2N) VOAs.
Generalized Schur indices of N=2 class S theories are expressed using eigenfunctions of non-relativistic elliptic Calogero-Moser models, with extensions claimed for N=1 SCFTs via limits of models like Inozemtsev.
In the SU(2) maximal SYM theory, some fortuitous cohomologies are lifted by 1-loop corrections while the lightest and hairy versions are not, yielding at least 1.2% higher entropy for classical cohomologies than for strictly protected states in the Cardy limit.
In a toy qubit model of quarks, baryons are fortuitous with exponential counting and super-exponential complexity while mesons are monotone with polynomial counting and power-law complexity.
Near-EVH limits of AdS6 and AdS7 black holes produce conformally related lower-dimensional black hole solutions in EMMD gravity, opening a potential path to microscopic entropy counting for non-AdS black holes via higher-dimensional AdS/CFT.
A procedure dresses supergravitons with singletons to extend the BPS gravity-sector spectrum in AdS3/CFT2, yielding affine multiplets that match the D1-D5 CFT better after deformation up to higher levels.
The complex saddles of the ABJM index are interpreted through instability of wrapped M5-branes in the dual gravity theory.
citing papers explorer
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Half-BPS Boundaries and the RG-Wall of $\mathcal{N}=2$ $SU(N)$ SYM
A massive deformation of the T[SU(N)] theory is identified as the 3d SCFT realizing the RG-wall and half-BPS boundaries in 4d N=2 SU(N) SYM.
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Two roads to fortuity in ABJM theory
Enumerates 244 fortuitous operators in ABJM theory and identifies a truncation matching the BMN subsector of N=4 SYM to lift an infinite tower of representatives.
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Generalised 4d Partition Functions and Modular Differential Equations
Generalized Schur partition functions Z_USp(2N)(q; alpha) for 4d N=2 USp(2N) theories satisfy order-(N+1) MLDEs with vanishing Wronskian index, alpha fixing MLDE parameters, with links to RCFT characters and a conjecture on quantum monodromy traces.
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Fermionic extensions of $W$-algebras via 3d $\mathcal{N}=4$ gauge theories with a boundary
Constructs fermionic extensions of W-algebras W^{-N+1}(sl_N, f_sub) via BRST cohomology in 3d N=4 abelian gauge theories and explicitly computes the N=3 case as an extension of the Bershadsky-Polyakov algebra.
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Fermionic trace relations and supersymmetric indices at finite $N$
The supersymmetric index in a one-fermion matrix model for N=4 SYM is independent of N due to exact cancellations between bosonic and fermionic trace relations.
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Chaos of Berry curvature for BPS microstates
Berry curvature of BPS states is random-matrix-like for supersymmetric black hole microstates but non-random and often zero for horizonless geometries, offering a chaos diagnostic in degenerate sectors.
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Refined 3D index
A refined 3D index is defined by adding flavor symmetry gradings to the superconformal index of T[M], yielding an explicit infinite-sum formula from Dehn surgery that is claimed to be a strictly stronger invariant than the standard 3D index.
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Unitary matrix models, quantized symmetric functions and spin chain
Unitary matrix models are mapped to vacuum correlators of quantized symmetric functions in the N-magnon sector of a spin chain via Schur orthogonality.
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Gravitational index, black hole saddle degeneracy, and one-form symmetry
The |G|-fold degeneracy of supersymmetric AdS5 black hole index saddles is fixed by the flux-quantized BF coupling of the bulk one-form symmetry and persists unmodified in the decompactified black-brane limit.
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Complex BPS Black Holes in AdS$_3\times S^3$
Constructs complex BTZ x S3 saddles for the supersymmetric index in AdS3 x S3 supergravity, matching supersymmetry requirements through two-center 4D solutions with complex charges and 6D black strings.
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Finite scalar field theory with SU(1,1) spacetime symmetry from near-BPS limits of $\mathcal{N}=4$ SYM
A non-Lorentzian scalar QFT with SU(1,1) symmetry obtained from N=4 SYM is finite at all orders in perturbation theory.
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(Un)solvable Matrix Models for BPS Correlators
Proposes complex matrix models for BPS correlators in N=4 SYM, relating eigenvalue distributions to LLM droplet shapes and enabling computations of one-point functions and three-point correlators via reductions to known models.
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Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
High-temperature limits on higher sheets of the superconformal index for (A1,A2n) Argyres-Douglas theories yield Gang-Kim-Stubbs 3d N=2 theories whose boundaries support Virasoro minimal model VOAs M(2,2n+3) and associated MTCs.
-
Quarter-indices for basic ortho-symplectic corners
Exact quarter-indices for basic ortho-symplectic corners in N=4 SYM are obtained in closed form, proven equal under duality, and interpreted as vacuum characters of BCD W-algebras and osp(1|2N) VOAs.
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On non-relativistic integrable models and 4d SCFTs
Generalized Schur indices of N=2 class S theories are expressed using eigenfunctions of non-relativistic elliptic Calogero-Moser models, with extensions claimed for N=1 SCFTs via limits of models like Inozemtsev.
-
Quantum black hole cohomologies
In the SU(2) maximal SYM theory, some fortuitous cohomologies are lifted by 1-loop corrections while the lightest and hairy versions are not, yielding at least 1.2% higher entropy for classical cohomologies than for strictly protected states in the Cardy limit.
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Fortuity and Complexity in a Simple Quark Model
In a toy qubit model of quarks, baryons are fortuitous with exponential counting and super-exponential complexity while mesons are monotone with polynomial counting and power-law complexity.
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Probing decoupled Throats of AdS$_{D}$ Black Holes in $D=6,7$
Near-EVH limits of AdS6 and AdS7 black holes produce conformally related lower-dimensional black hole solutions in EMMD gravity, opening a potential path to microscopic entropy counting for non-AdS black holes via higher-dimensional AdS/CFT.
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Towering Gravitons in AdS$_3$/CFT$_2$
A procedure dresses supergravitons with singletons to extend the BPS gravity-sector spectrum in AdS3/CFT2, yielding affine multiplets that match the D1-D5 CFT better after deformation up to higher levels.
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A gravity interpretation for the complex Euclidean saddles of the ABJM index
The complex saddles of the ABJM index are interpreted through instability of wrapped M5-branes in the dual gravity theory.
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