Fortuity in the D1-D5 system

TL;DR

This paper reformulates the D1-D5 CFT lifting problem as a supercharge cohomology problem, classifies BPS states, and connects them to holographic duals like black hole bound states and string excitations.

Contribution

It introduces a new cohomology-based framework for enumerating BPS states in the D1-D5 system and explicitly constructs these states for N=2, linking to holographic duals.

Findings

Defined monotone and fortuitous cohomology classes in deformed T^4 orbifold theory

Constructed explicit cohomology for N=2 and matched it to BPS partition function

Described assembly of BPS states across different N and their holographic interpretations

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.