Integrable Deformations of $\hat{c}=1$ Strings in Flux Backgrounds

TL;DR

This paper investigates deformations of two-dimensional type 0A string theory with flux backgrounds, revealing a complex Toda hierarchy and analyzing phase transitions and critical phenomena.

Contribution

It introduces a novel complexified Toda hierarchy constrained by new holomorphic string equations for deformed 0A strings with flux backgrounds.

Findings

Derived non-holomorphic transcendental equations for string susceptibility.

Solved the hierarchy constraints in the classical limit for general flux and tachyon condensate.

Explored phase structure and critical behavior of the deformed string theory.

Abstract

We study d=2 0A string theory perturbed by tachyon momentum modes in backgrounds with non-trivial tachyon condensate and Ramond-Ramond (RR) flux. In the matrix model description, we uncover a complexified Toda lattice hierarchy constrained by a pair of novel holomorphic string equations. We solve these constraints in the classical limit for general RR flux and tachyon condensate. Due to the non-holomorphic nature of the tachyon perturbations, the transcendental equations which we derive for the string susceptibility are manifestly non-holomorphic. We explore the phase structure and critical behavior of the theory.