Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux

TL;DR

This paper derives finite-gap equations and Bethe ansatz for superstrings on AdS_3 x S^3 x T^4 with mixed fluxes, analyzing the spectrum and quantum corrections, and explores classical solutions like giant magnons.

Contribution

It introduces finite-gap and Bethe ansatz equations for strings with mixed fluxes, including new dressing phases and one-loop corrections, extending previous pure RR results.

Findings

Finite-gap equations describe the classical spectrum.

All-loop Bethe ansatz matches the finite-gap equations.

New dressing phases differ from pure RR case.

Abstract

We study superstrings on AdS_3 x S^3 x T^4 supported by a combination of Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz three form fluxes, and construct a set of finite-gap equations that describe the classical string spectrum. Using the recently proposed all-loop S-matrix we write down the all-loop Bethe ansatz equations for the massive sector. In the thermodynamic limit the Bethe ansatz reproduces the finite-gap equations. As part of this derivation we propose expressions for the leading order dressing phases. These phases differ from the well-known Arutyunov-Frolov-Staudacher phase that appears in the pure Ramond-Ramond case. We also consider the one-loop quantization of the algebraic curve and determine the one-loop corrections to the dressing phases. Finally we consider some classical string solutions including finite size giant magnons and circular strings.