RG Flows from Super-Liouville Theory to Critical Ising Model

TL;DR

This paper investigates an integrable deformation of super-Liouville theory that flows to the critical Ising model, revealing a supersymmetric sinh-Gordon model with a Goldstino particle and proposing its exact S-matrix.

Contribution

It introduces a new integrable deformation connecting super-Liouville theory to the critical Ising model and provides the exact S-matrix for the Goldstino particle.

Findings

Identified the IR fixed point as the critical Ising model.

Proposed the exact S-matrix for the Goldstino.

Validated the model using thermodynamic Bethe ansatz equations.

Abstract

We study an integrable deformation of the super-Liouville theory which generates a RG flows to the critical Ising model as the IR fixed point. This model turns out to be a supersymmetric sinh-Gordon model with spontaneously broken N=1 supersymmetry. The resulting massless Goldstino is the only stable on-shell particle which controls the IR behaviours. We propose the exact $S$-matrix of the Goldstino and compare associated thermodynamic Bethe ansatz equations with the quantization conditions derived from the reflection amplitudes of the the super-Liouville theory to provide nonperturbative checks for both the (NS) and the (R) sectors.