Thermodynamic Bethe Ansatz for N = 1 supersymmetric theories

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.

Trigonometric S Matrices, Affine Toda Solitons and Supersymmetry

“…In [39] Melzer conjectured a connection between the N = 2 and N = 1 scattering theories via a "folding" of their TBA systems (see also [40]). In [6] Moriconi and Schoutens completed the Thermodynamic Bethe Ansatz for these N = 1 supersymmetric theories and were able to prove Melzer's conjecture. This folding procedure takes the following form:…”

Reflection matrices for integrable N = 1 supersymmetric theories

“…In addition, it may be observed that supersymmetric factorizable S-matrices are among the simplest ones that are non-diagonal. Certain procedures that are problematic for non-diagonal S-matrices, such as for example the Thermodynamic Bethe Ansatz (TBA), become manageable when the non-diagonal S-matrices are controled by an underlying symmetry such as supersymmetry [7][8][9]. This point was made very clearly in [10,8,9], where it was shown that N = 1 supersymmetry leads to a 'free fermion condition' for certain two-particle S-matrices, and that this free fermion condition makes it possible to perform the TBA analysis in closed form.…”

The scaling supersymmetric Yang–Lee model with boundary

“…(3.8), (3.9). TBA analysis [20], [21] shows that this S matrix correctly reproduces the central charge of the unperturbed CFT.…”

“…In an effort to provide more such examples, we consider here the boundary version of the bulk scaling supersymmetric Yang-Lee (SYL) model [19]- [21]. This model is arguably the simplest nontrivial supersymmetric quantum field theory.…”