Integrable Superstrings on the Squashed Three-sphere

TL;DR

This paper demonstrates that type II superstring theory on a specific background involving a squashed three-sphere is classically integrable, with a superalgebra structure despite broken spacetime symmetries.

Contribution

It explicitly derives the Green-Schwarz action for the background and reveals the hidden integrable structure with a psu(1,1|2) superalgebra.

Findings

Model is classically integrable.

Currents generate a psu(1,1|2) superalgebra.

Spacetime isometries are broken by squashing.

Abstract

In this note we study type II superstring theory on the direct product of AdS3, the squashed three-sphere and a four-torus (AdS3 \times SqS3 \times T4). We derive explicitly the Green-Schwarz action and discuss in detail the hidden integrable structure corresponding to local and non-local currents. We find that the model is classically integrable and that the currents generate a full psu(1, 1|2) superalgebra, even though the corresponding spacetime isometries are broken by the squashing.