Twisted kink dynamics in multiflavor chiral Gross-Neveu model

TL;DR

This paper revisits the multiflavor chiral Gross-Neveu model in the large N_c limit, providing a clearer analytical solution for twisted kink and breather interactions by isolating key factors and introducing a new matrix inverse identity.

Contribution

It presents a reformulation of the known analytical solutions for twisted kinks and breathers, highlighting the role of twist matrices and deriving a new identity for matrix inverses.

Findings

Analytical solution for time-dependent interactions of twisted kinks and breathers.

Isolation of (x,t)-dependent factors from constant coefficients and twist matrices.

Introduction of a new matrix inverse identity derived from determinant formulas.

Abstract

The Gross-Neveu model with ${\rm U}_L(N_f)\times{\rm U}_R(N_f)$ chiral symmetry is reconsidered in the large $N_c$ limit. The known analytical solution for the time dependent interaction of any number of twisted kinks and breathers is cast into a more revealing form. The ($x,t$)-dependent factors are isolated from constant coefficients and twist matrices. These latter generalize the twist phases of the single flavor model. The crucial tool is an identity for the inverse of a sum of two square matrices, derived from the known formula for the determinant of such a sum.