Scattering and Thermodynamics of Integrable N=2 Theories

TL;DR

This paper investigates the scattering and thermodynamic properties of N=2 supersymmetric integrable theories, providing exact soliton spectra, S-matrices, and ground-state energies, and exploring their conformal limits and extensions.

Contribution

It introduces a comprehensive analysis of N=2 integrable theories with broken Z_n symmetry, including exact soliton masses, S-matrices, and thermodynamic results, and proposes a conjecture on their soliton content in broader classes.

Findings

Exact soliton masses match affine SU(n) Toda models.

Ground-state energies are calculated exactly and match conformal limits.

S-matrices are constructed using Landau-Ginzburg descriptions.

Abstract

We study $N$=2 supersymmetric integrable theories with spontaneously-broken \Zn\ symmetry. They have exact soliton masses given by the affine $SU(n)$ Toda masses and fractional fermion numbers given by multiples of $1/n$. The basic such $N$=2 integrable theory is the $A_n$-type $N$=2 minimal model perturbed by the most relevant operator. The soliton content and exact S-matrices are obtained using the Landau-Ginzburg description. We study the thermodynamics of these theories and calculate the ground-state energies exactly, verifying that they have the correct conformal limits. We conjecture that the soliton content and S-matrices in other integrable \Zn\ $N$=2 theories are given by the tensor product of the above basic $N$=2 \Zn\ scattering theory with various $N$=0 theories. In particular, we consider integrable perturbations of $N$=2 Kazama-Suzuki models described by generalized Chebyshev potentials, $CP^{n-1}$ sigma models, and $N$=2 sine-Gordon and its affine Toda generalizations.