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Fortuity in the D1-D5 system

Chi-Ming Chang, Ying-Hsuan Lin, Haoyu Zhang

Abstract

We reformulate the lifting problem in the D1-D5 CFT as a supercharge cohomology problem, and enumerate BPS states according to the fortuitous/monotone classification. Working in the deformed $T^4$ symmetric orbifold theory, we give precise definitions of monotone and fortuitous cohomology classes generalizing the definitions in \cite{Chang:2024zqi} and illustrate them in the $N=1$ theory. For $N=2$, we construct the cohomology explicitly and match it to the exact BPS partition function. We further describe how to assemble BPS states at smaller $N$ into BPS states at larger $N$, and interpret their holographic duals as black hole bound states and massive stringy excitations on smooth horizonless (e.g. Lunin-Mathur) geometries.

Fortuity in the D1-D5 system

Abstract

We reformulate the lifting problem in the D1-D5 CFT as a supercharge cohomology problem, and enumerate BPS states according to the fortuitous/monotone classification. Working in the deformed symmetric orbifold theory, we give precise definitions of monotone and fortuitous cohomology classes generalizing the definitions in \cite{Chang:2024zqi} and illustrate them in the theory. For , we construct the cohomology explicitly and match it to the exact BPS partition function. We further describe how to assemble BPS states at smaller into BPS states at larger , and interpret their holographic duals as black hole bound states and massive stringy excitations on smooth horizonless (e.g. Lunin-Mathur) geometries.
Paper Structure (23 sections, 144 equations, 4 tables)

This paper contains 23 sections, 144 equations, 4 tables.

Table of Contents

  1. Introduction and summary of results
  2. Review of the D1-D5 CFT
  3. Symmetric orbifold of the $T^4$ CFT
  4. BPS states at the orbifold point
  5. Lifting under conformal perturbation theory
  6. Modified index
  7. Exact BPS partition function at $N=2$
  8. Lifting as a supercharge cohomology problem
  9. Deformed $Q$-action on the free BPS sector
  10. Explicit cohomology representatives at $N=2$
  11. Monotone and fortuitous cohomologies
  12. Classification
  13. Example: classification at $N=1$
  14. Monotone stringy exclusion principle
  15. Composite BPS states
  16. ...and 8 more sections

Theorems & Definitions (3)

  • Conjecture 1: Non-renormalization
  • Definition 1: Monotone and fortuitous
  • Definition 2: Absolute monotone