Sub-leading Structures in Superconformal Indices: Subdominant Saddles and Logarithmic Contributions

Abstract

We systematically study various sub-leading structures in the superconformal index of $\mathcal{N}=4$ supersymmetric Yang-Mills theory with SU($N$) gauge group. We concentrate in the superconformal index description as a matrix model of elliptic gamma functions and in the Bethe-Ansatz presentation. Our saddle-point approximation goes beyond the Cardy-like limit and we uncover various saddles governed by a matrix model corresponding to SU($N$) Chern-Simons theory. The dominant saddle, however, leads to perfect agreement with the Bethe-Ansatz approach. We also determine the logarithmic correction to the superconformal index to be $\log N$, finding precise agreement between the saddle-point and Bethe-Ansatz approaches in their respective approximations. We generalize the two approaches to cover a large class of 4d $\mathcal{N}=1$ superconformal theories. We find that also in this case both approximations agree all the way down to a universal contribution of the form $\log N$. The universality of this last result constitutes a robust signature of this ultraviolet description of asymptotically AdS${}_5$ black holes and could be tested by low-energy IIB supergravity.

55 pages, 9 figures; v2: minor revisions; v3: minor revisions in p.14,20,23; v4: minor revisions in Appendix A; v5: correct minor typos in Appendix C

References in corpus (46)

• An Index for 4 dimensional Super Conformal Theories
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• Counting chiral primaries in N=1 d=4 superconformal field theories
• Gauge Theories from Toric Geometry and Brane Tilings
• Black hole microstates in AdS${}_4$ from supersymmetric localization
• An Infinite Family of Superconformal Quiver Gauge Theories with Sasaki-Einstein Duals
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS${}_5$ black holes
• ABJM theory as a Fermi gas
• Worldsheet Derivation of a Large N Duality
• Matrix Model as a Mirror of Chern-Simons Theory
• Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates
• Cardy Formulae for SUSY Theories in d=4 and d=6
• An extremization principle for the entropy of rotating BPS black holes in AdS${}_5$
• Black holes in 4d $\mathcal{N}=4$ Super-Yang-Mills
• The asymptotic growth of states of the 4d N=1 superconformal index
• Supersymmetric partition functions and the three-dimensional A-twist
• Quantum Black Hole Entropy from 4d Supersymmetric Cardy formula
• Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories
• Cardy-like asymptotics of the 4d $\mathcal{N}=4$ index and AdS${}_5$ blackholes
• A One-loop Test of Quantum Black Holes in Anti de Sitter Space
• Microscopic Entropy of Rotating Electrically Charged AdS${}_4$ Black Holes from Field Theory Localization
• High-temperature asymptotics of supersymmetric partition functions
• Supersymmetric phases of 4d N=4 SYM at large N
• Asymptotic growth of the 4d $\mathcal{N}=4$ index and partially deconfined phases
• F-theorem, duality and SUSY breaking in one-adjoint Chern-Simons-Matter theories
• Superconformal indices at large $N$ and the entropy of AdS${}_5$ $\times$ SE${}_5$ black holes
• The Cardy limit of the topologically twisted index and black strings in AdS${}_5$
• A Bethe Ansatz type formula for the superconformal index
• The Spectral Curve of the Lens Space Matrix Model
• Universal Spinning Black Holes and Theories of Class $\mathcal{R}$
• Rotating Black Hole Entropy from M5-branes
• A note on the entropy of rotating BPS AdS${}_7\times S^4$ black holes
• Toward Microstate Counting Beyond Large N in Localization and the Dual One-loop Quantum Supergravity
• The large-$N$ limit of the 4d $\mathcal{N}=1$ superconformal index
• Black hole entropy function for toric theories via Bethe Ansatz
• The topologically twisted index of $\mathcal{N}=4$ super-Yang-Mills on $T^2\times S^2$ and the elliptic genus
• Cardy Formula for 4d SUSY Theories and Localization
• Precision Microstate Counting for the Entropy of Wrapped M5-branes
• AdS${}_5$ Black Hole Entropy near the BPS Limit
• AdS${}_7$ Black-Hole Entropy and 5D $\mathcal{N}=2$ Yang-Mills
• Gravitational Cardy Limit and AdS Black Hole Entropy
• The Topologically Twisted Index in the 't Hooft Limit and the Dual AdS${}_4$ Black Hole Entropy
• The 5d Superconformal Index at Large $N$ and Black Holes
• Toward an Effective CFT${}_2$ from $\mathcal{N}=4$ Super Yang-Mills and Aspects of Hawking Radiation

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• Residues, modularity, and the Cardy limit of the 4d $\mathcal{N}=4$ superconformal index
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• Higher-Derivative Corrections and AdS${}_5$ Black Holes
• Exact Stringy Microstates from Gauge Theories
• $SL(3,\mathbb{Z})$ Modularity and New Cardy Limits of the $\mathcal{N}=4$ Superconformal Index
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• Large $N$ Superconformal Indices for 3d Holographic SCFTs
• Decomposition of BPS Moduli Spaces and Asymptotics of Supersymmetric Partition Functions
• Supersymmetric phases of AdS${}_4$/CFT${}_3$
• Exact QFT duals of AdS black holes
• Logarithmic Corrections to the Entropy of Rotating Black Holes and Black Strings in AdS${}_5$
• Higher-derivative corrections to flavoured BPS black hole thermodynamics and holography
• Non-topological logarithmic corrections in minimal gauged supergravity
• Quantum Phases of $4d$ $SU(N)$ $\mathcal{N}=4$ SYM
• Microscopic Entropy of AdS${}_3$ Black Holes Revisited
• Universal Entropy and Hawking Radiation of Near-Extremal AdS${}_4$ Black Holes
• The large-$N$ limit of 4d superconformal indices for general BPS charges
• Supersymmetric Grey Galaxies, Dual Dressed Black Holes and the Superconformal Index
• Anomaly Matching Across Dimensions and Supersymmetric Cardy Formulae
• Expanding on the Cardy-like limit of the superconformal index of 4d $\mathcal{N}=1$ ABCD SCFTs
• S-duality in the Cardy-like limit of the superconformal index
• Confinement and Graded Partition Functions for $\mathcal{N}=4$ SYM
• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
• The topologically twisted index of $\mathcal{N}=4$ SU($N$) Super-Yang-Mills theory and a black hole Farey tail
• Wrapped M5-branes and AdS${}_5$ Black Holes
• Hawking-Page transition on a spin chain
• Supersymmetric zeta functions and determinants
• Explorations of Universality in the Entropy and Hawking Radiation of Non-Extremal Kerr AdS${}_4$ Black Holes
• Off-shell phase diagram of BPS black holes in AdS${}_5$