Chiral symmetry breaking patterns in the U_L(n)xU_R(n) meson model

TL;DR

This paper explores the patterns of chiral symmetry breaking in the U_L(n)xU_R(n) meson model, demonstrating the existence of new minima and confirming that the typical symmetry breaking pattern U_L(n)xU_R(n) to U_V(n) is favored in the strong interaction regime.

Contribution

It identifies new classes of minima in the effective potential and confirms the standard symmetry breaking pattern using a nonperturbative approach, supporting the Vafa-Witten theorem.

Findings

Existence of new minima in the effective potential for arbitrary n

Confirmation of U_L(n)xU_R(n) to U_V(n) symmetry breaking in strong interaction regimes

Validation of the Vafa-Witten theorem within an effective meson model

Abstract

Chiral symmetry breaking patterns are investigated in the U_L(n)xU_R(n) meson model. It is shown that new classes of minima of the effective potential belonging to the center of the Lie algebra exist for arbitrary flavor number n. The true ground state of the system is searched nonperturbatively and although multiple local minima of the effective potential may exist, it is argued that in regions of the parameter space applicable for the strong interaction, strictly a U_L(n)xU_R(n)->U_V(n) spontaneous symmetry breaking is possible. The reason behind this is the existence of a discrete subset of axial symmetries, which connects various U_V(n) symmetric vacua of the theory. The results are in agreement with the Vafa-Witten theorem of QCD, illustrating that it remains valid, even without gauge fields, for an effective model of the strong interaction.