BPS spectrum on AdS$_3\times $S$^3 \times $S$^3 \times $S$^1$

TL;DR

This paper determines the BPS spectrum of string theory on AdS3×S3×S3×S1 using world-sheet WZW models, revealing that only states with equal spins in the two SU(2) algebras are BPS, resolving longstanding puzzles.

Contribution

It provides a detailed analysis showing that both string theory and supergravity only have BPS states with equal spins, clarifying previous ambiguities in the spectrum.

Findings

Only BPS states with j^+ = j^- are present in string theory.

Supergravity also only admits states with j^+ = j^- as BPS.

Resolves longstanding discrepancies in the BPS spectrum understanding.

Abstract

The BPS spectrum of string theory on AdS$_3\times {\rm S}^3 \times {\rm S}^3 \times {\rm S}^1$ is determined using a world-sheet description in terms of WZW models. It is found that the theory only has BPS states with $j^+ = j^-$ where $j^{\pm}$ refer to the spins of the $\mathfrak{su}(2)$ algebras of the large ${\cal N}=4$ superconformal algebra. We then re-examine the BPS spectrum of the corresponding supergravity and find that, in contradistinction to previous claims in the literature, also in supergravity only the states with $j^+=j^-$ are BPS. This resolves a number of long-standing puzzles regarding the BPS spectrum of string theory and supergravity in this background.