Thermodynamic Bethe Ansatz for N = 1 Supersymmetric Theories

TL;DR

This paper develops the Thermodynamic Bethe Ansatz for N=1 supersymmetric integrable theories in 1+1 dimensions, confirming a conjecture that these systems are folded versions of N=2 supersymmetric TBA systems.

Contribution

The paper constructs the TBA for N=1 supersymmetric theories using their S-matrices and proves Melzer's conjecture relating them to N=2 systems.

Findings

Confirmed the TBA for N=1 theories using free fermion condition.

Proved N=1 TBA systems are folded versions of N=2 systems.

Validated Melzer's conjecture on the relation between N=1 and N=2 TBA systems.

Abstract

We study a series of $N\!=\!1$ supersymmetric integrable particle theories in $d=1+1$ dimensions. These theories are represented as integrable perturbations of specific $N\!=\!1$ superconformal field theories. Starting from the conjectured $S$-matrices for these theories, we develop the Thermodynamic Bethe Ansatz (TBA), where we use that the 2-particle $S$-matrices satisfy a free fermion condition. Our analysis proves a conjecture by E.~Melzer, who proposed that these $N\!=\!1$ supersymmetric TBA systems are ``folded'' versions of $N\!=\!2$ supersymmetric TBA systems that were first studied by P.~Fendley and K.~Intriligator.