Violation of Parity and Flavor Symmetries in a Nambu-Jona-Lasinio Model

TL;DR

This paper investigates a lattice Nambu-Jona-Lasinio model demonstrating that its ground state breaks parity and flavor symmetries, highlighting the role of chiral symmetry without Wilson terms.

Contribution

It constructs a ground state in a lattice NJL model that explicitly breaks parity and flavor symmetries, emphasizing chiral symmetry's role in this violation.

Findings

Ground state breaks parity symmetry.

Ground state breaks flavor symmetry.

Chiral symmetry is crucial for symmetry violation.

Abstract

We study a lattice Nambu-Jona-Lasinio model with certain continuous chiral and two-flavor symmetries. For the Hamiltonian of the model, we construct a ground state which breaks the parity and flavor symmetries. In our argument, the chiral symmetry plays a crucial role for proving the violation of the parity and flavor symmetries, although the model does not contain the so-called Wilson term.