BPS kinks in the Gross-Neveu model

TL;DR

This paper determines the exact spectrum, degeneracies, and S matrix of kinks in the two-dimensional Gross-Neveu model, revealing novel BPS states and their relation to supersymmetry, with implications for understanding non-perturbative phenomena.

Contribution

It provides the first exact spectrum, degeneracies, and S matrix for BPS kinks in the Gross-Neveu model, linking them to generalized supersymmetry.

Findings

Spectrum contains 2^{N/2} kinks for any N.

Exact S matrix for the kinks is derived.

The free energy of the model is exactly computed.

Abstract

We find the exact spectrum and degeneracies for the Gross-Neveu model in two dimensions. This model describes N interacting Majorana fermions; it is asymptotically free, and has dynamical mass generation and spontaneous chiral symmetry breaking. We show here that the spectrum contains 2^{N/2} kinks for any $N$. The unusual \sqrt{2} in the number of kinks for odd $N$ comes from restrictions on the allowed multi-kink states. These kinks are the BPS states for a generalized supersymmetry where the conserved current is of dimension N/2; the N=3 case is the {\cal N}=1 supersymmetric sine-Gordon model, for which the spectrum consists of 2\sqrt{2} kinks. We find the exact S matrix for these kinks, and the exact free energy for the model.