Fortuity and R-charge concentration in the D1-D5 CFT

TL;DR

This paper explores special cohomology classes in the D1-D5 conformal field theory, revealing a concentration of R-charge and identifying explicit fortuitous classes through representation analysis.

Contribution

It constructs explicit fortuitous classes in the D1-D5 CFT and conjectures their relation to maximal representations and R-charge concentration phenomena.

Findings

Explicit fortuitous classes constructed for N=2 and N=3 theories

Largest representation classes are conjectured to be fortuitous

Evidence of R-charge concentration phenomenon in D1-D5 CFT

Abstract

We investigate finite-$N$ BPS cohomology in the D1--D5 CFT, focusing on the sector of fortuitous classes. Analyzing the supercharge cochain complexes in the $N=2$ and $N=3$ theories, we construct several explicit fortuitous classes. We study the decomposition of these cohomology classes into ${\rm SU}(2)_a\times {\rm SU}(2)_b$ representations and conjecture that, at fixed holomorphic weight, those transforming in the largest representation are necessarily fortuitous. Our results also provide strong evidence that the $R$-charge concentration phenomenon extends to the D1--D5 CFT.