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

Abstract

The BPS spectrum of string theory on AdS${}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$ 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 $\mathcal{N}=4$ 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.

36 pages; ancillary file included, v2: changed statement about spectrally flowed sectors, minor typos corrected

References in corpus (2)

• Higher Spins & Strings
• An Index for 2D field theories with large N=4 superconformal symmetry

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