A New Supersymmetry Index for the D1-D5 CFT

Abstract

We propose a new supersymmetry index for the D1-D5 CFT for $T^4$, relevant to the AdS${}_3$/CFT${}_2$ correspondence. In a novel formulation of symmetric orbifold CFTs based on the Schur-Weyl duality, we show how this index can be naturally described and its protection is argued based on the detailed nature of exactly marginal operators in these theories. This index is a one-parameter generalization of the standard index and gives more fine-grained information about the structure of microstates than previously available. We demonstrate precise matching of the new index between supergravity and CFT below the black-hole threshold, where the standard index -- the modified elliptic genus -- is trivial. Above the threshold, we uncover a decomposition of black-hole microstates into distinct sectors, invisible to the modified elliptic genus.

arXiv comment6 pages + Appendix, 3 figures. v2: Changes made to the definition of the proposed index and clarification about protection given. References added. v3: Minor corrections in line with published version

References in corpus (37)

• Microscopic Origin of the Bekenstein-Hawking Entropy
• AdS3 Black Holes and a Stringy Exclusion Principle
• D--branes and Spinning Black Holes
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Microscopic Formulation of Black Holes in String Theory
• Elliptic Genera of Symmetric Products and Second Quantized Strings
• Comparing decay rates for black holes and D-branes
• Six-Dimensional Supergravity on S^3 X AdS_3 and 2d Conformal Field Theory
• D-branes and Fat Black Holes
• Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS${}_5$ black holes
• Correlation functions for M^N/S_N orbifolds
• Split States, Entropy Enigmas, Holes and Halos
• Diagrams for Symmetric Product Orbifolds
• Spectrum of D=6, N=4b Supergravity on AdS_3 x S^3
• Anti-de Sitter Space and the Center of the Gauge Group
• A holographic dual for string theory on ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$
• Proving the PP-Wave/CFT_2 Duality
• Extremal Correlators and Hurwitz Numbers in Symmetric Product Orbifolds
• Large N Elliptic Genus and AdS/CFT Correspondence
• Phase transitions in symmetric orbifold CFTs and universality
• Moulting Black Holes
• Emission from the D1D5 CFT: Higher Twists
• Superstrata
• Lifting of D1-D5-P states
• The Perturbation Spectrum of Black Holes in N=8 Supergravity
• No entropy enigmas for N=4 dyons
• Lifting at higher levels in the D1D5 CFT
• Lifting 1/4-BPS States in $Ad{S}_3\times S^3\times T^4$
• Lifting of level-1 states in the D1D5 CFT
• $\mathcal{N}=2$ Minimal Models: A Holographic Needle in a Symmetric Orbifold Haystack
• BPS Chaos
• Universal lifting in the D1-D5 CFT
• The Stranger Things of Symmetric Product Orbifold CFTs
• Lifting of states in 2-dimensional $N=4$ supersymmetric CFTs
• The Holographic Landscape of Symmetric Product Orbifolds
• $S_N$ Orbifolds and String Interactions
• Symmetric Product Orbifold Universality and the Mirage of an Emergent Spacetime

Cited by in corpus (1)

• The Resolved Elliptic Genus and the D1-D5 CFT