Superstrings in AdS(2)xS(2)xT(6)

TL;DR

This paper investigates the classical integrability of the type IIB superstring on AdS(2)xS(2)xT(6), demonstrating integrability to quadratic fermions and proposing Bethe ansatz equations for certain quantum states.

Contribution

It shows that the superstring model on AdS(2)xS(2)xT(6) is classically integrable and admits a consistent truncation to the supercoset sigma-model, extending understanding of integrability in this background.

Findings

The superstring model is classically integrable to quadratic order in fermions.

A consistent classical truncation to the supercoset sigma-model is possible.

Proposed asymptotic Bethe ansatz equations for certain quantum string states.

Abstract

We consider the type IIB Green-Schwarz superstring theory on AdS(2)xS(2)xT(6) supported by homogeneous Ramond-Ramond 5-form flux and its type IIA T-duals. One motivation is to understand the solution of this theory based on integrability. This background is a limit of a 1/4 supersymmetric supergravity solution describing four intersecting D3-branes and represents a consistent embedding of AdS(2)xS(2) into critical superstring theory. Its AdS(2)xS(2) part with corresponding fermions can be described by a classically integrable PSU(1,1|2)/SO(1,1)xU(1) supercoset sigma-model. We point out that since the RR 5-form field has non-zero components along the 6-torus directions one cannot, in general, factorize the 10d superstring theory into the supercoset part plus 6 bosons and 6 additional massless fermions. Still, we demonstrate that the full superstring model (i) is classically integrable, at least to quadratic order in fermions, and (ii) admits a consistent classical truncation to the supercoset part. Following the analogy with other integrable backgrounds and starting with the finite-gap equations of the PSU(1,1|2)/SO(1,1)xU(1) supercoset we propose a set of asymptotic Bethe ansatz equations for a subset of the quantum string states.