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Holographic covering and the fortuity of black holes

Chi-Ming Chang, Ying-Hsuan Lin

TL;DR

The work introduces a holographic covering framework to classify BPS states in holographic CFTs into monotone and fortuitous categories using supercharge cohomology. It argues that monotone BPS states map to perturbative, smooth horizonless bulk geometries, while fortuitous BPS states account for the majority of black hole microstates and entropy, with fortuitous states vastly outnumbering monotone ones at large N. The authors provide evidence from ${\cal N}=4$ SYM and symmetric product orbifolds by quantizing classical moduli spaces of LLM/LM geometries, recovering finite-N BPS spectra and linking trace relations to the holographic picture. The results suggest a new route to microstate construction and raise open questions about extending the framework to less supersymmetric settings and to continuous-N algebras.

Abstract

We propose a classification of BPS states in holographic CFTs into monotone and fortuitous, based on their behaviors in the large $N$ limit. Intuitively, monotone BPS states form infinite sequences with increasing rank $N$, while fortuitous ones exist within finite ranges of consecutive ranks. A precise definition is formulated using supercharge cohomology. We conjecture that under the AdS/CFT correspondence, monotone BPS states are dual to smooth horizonless geometries, and fortuitous ones are responsible for typical black hole microstates and give dominant contributions to the entropy. We present supporting evidence for our conjectures in the ${\cal N}=4$ SYM and symmetric product orbifolds.

Holographic covering and the fortuity of black holes

TL;DR

The work introduces a holographic covering framework to classify BPS states in holographic CFTs into monotone and fortuitous categories using supercharge cohomology. It argues that monotone BPS states map to perturbative, smooth horizonless bulk geometries, while fortuitous BPS states account for the majority of black hole microstates and entropy, with fortuitous states vastly outnumbering monotone ones at large N. The authors provide evidence from SYM and symmetric product orbifolds by quantizing classical moduli spaces of LLM/LM geometries, recovering finite-N BPS spectra and linking trace relations to the holographic picture. The results suggest a new route to microstate construction and raise open questions about extending the framework to less supersymmetric settings and to continuous-N algebras.

Abstract

We propose a classification of BPS states in holographic CFTs into monotone and fortuitous, based on their behaviors in the large limit. Intuitively, monotone BPS states form infinite sequences with increasing rank , while fortuitous ones exist within finite ranges of consecutive ranks. A precise definition is formulated using supercharge cohomology. We conjecture that under the AdS/CFT correspondence, monotone BPS states are dual to smooth horizonless geometries, and fortuitous ones are responsible for typical black hole microstates and give dominant contributions to the entropy. We present supporting evidence for our conjectures in the SYM and symmetric product orbifolds.
Paper Structure (14 sections, 1 theorem, 73 equations, 1 figure)

This paper contains 14 sections, 1 theorem, 73 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Holographic covering and BPS taxonomy
  3. What is a holographic CFT?
  4. Holographic covering hypothesis
  5. Monotone versus fortuitous sequences
  6. Lessons and conjectures
  7. Perturbative bulk Hilbert space
  8. Finite $N$ quotient from quantizing supergravity solutions
  9. On the fortuity of black holes
  10. Case studies
  11. ${\mathcal{N}}=4$ SYM and the deformation quantization of LLM geometries
  12. Symmetric product orbifolds and the quantization of LM geometries
  13. Discussions and open problems
  14. Canonical quantization of the LLM geometries

Key Result

Theorem 1

In the symmetry-refined long exact sequence eqn:LES, there exist the following bounds:

Figures (1)

  • Figure 1: Typical behaviors of sequences from lifting monotone and fortuitous BPS operators to larger $N$, where $\delta$ is the anomalous dimension. The dashed lines indicate their anomalous dimensions continued to non-integer $N$ in perturbation theory.

Theorems & Definitions (8)

  • Definition 1: Covering
  • Definition 2: Strictness
  • Definition 3: Covering symmetry
  • Definition 4: Monotone and fortuitous
  • Conjecture 1
  • Conjecture 2
  • Theorem 1
  • Conjecture 3