Spontaneous Symmetry Breaking in Discretized Light-Cone Quantization

TL;DR

This paper investigates spontaneous symmetry breaking in the discretized light-cone quantization of the Gross-Neveu model, revealing a nonzero fermion mass solution and discussing the model's vacuum and constituent picture.

Contribution

It introduces a scalar auxiliary field with a kinetic term to solve the zero mode constraint using the 1/N expansion, demonstrating symmetry breaking in the discretized framework.

Findings

Fermion acquires a nonzero mass, breaking discrete symmetry.

The Fock vacuum remains trivial and is an eigenstate of the Hamiltonian.

Infrared divergences are managed to obtain nontrivial solutions.

Abstract

Spontaneous symmetry breaking of the light-front Gross-Neveu model is studied in the framework of the discretized light-cone quantization. Introducing a scalar auxiliary field and adding its kinetic term, we obtain a constraint on the longitudinal zero mode of the scalar field. This zero-mode constraint is solved by using the $1/N$ expansion. In the leading order, we find a nontrivial solution which gives the fermion nonzero mass and thus breaks the discrete symmetry of the model. It is essential for obtaining the nontrivial solution to treat adequately an infrared divergence which appears in the continuum limit. We also discuss the constituent picture of the model. The Fock vacuum is trivial and an eigenstate of the light-cone Hamiltonian. In the large $N$ limit, the Hamiltonian consists of the kinetic term of the fermion with dressed mass and the interaction term of these fermions.