Lifting 1/4-BPS States in $AdS_3\times S^3 \times T^4$

TL;DR

This paper develops a second order conformal perturbation theory framework for symmetric orbifolds, enabling the study of how 1/4-BPS states in the D1-D5 system are lifted away from the orbifold point, revealing limitations of the supersymmetric index.

Contribution

It introduces a comprehensive perturbation theory method to analyze BPS state lifting in symmetric orbifolds at all orders in N.

Findings

Not all 1/4-BPS states are lifted at large N.

The supersymmetric index undercounts BPS states at generic moduli.

Framework applies to all orders in N for symmetric orbifolds.

Abstract

We establish a framework for doing second order conformal perturbation theory for the symmetric orbifold Sym$^N(T^4)$ to all orders in $N$. This allows us to compute how 1/4-BPS states of the D1-D5 system on $AdS_3\times S^3\times T^4$ are lifted as we move away from the orbifold point. As an application we confirm a previous observation that in the large $N$ limit not all 1/4-BPS states that can be lifted do get lifted. This provides evidence that the supersymmetric index actually undercounts the number of 1/4-BPS states at a generic point in the moduli space.