Year: 2001
Type: article
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 Bogomol'nyi-Prasad-Sommerfield states for a generalized supersymmetry where the conserved current is of dimension $N/2;$ the $N=3$ case is the $\mathcal{N}=1$ 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.
Authors: Paul Fendley, Hubert Saleur
Institution: University of Virginia
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2148820153