Fermionic Zero Modes and Spontaneous Symmetry Breaking on the Light Front

TL;DR

This paper investigates spontaneous symmetry breaking in a light-front sigma model with fermions, revealing a degenerate vacuum structure and the emergence of a Nambu-Goldstone boson due to fermion zero modes.

Contribution

It demonstrates how fermion zero modes induce spontaneous symmetry breaking and vacuum degeneracy in a light-front framework, providing new insights into symmetry dynamics.

Findings

Fermion zero modes prevent the vacuum from being annihilated by U(1) charges.

Degenerate vacuum states emerge due to zero mode dynamics.

Massless Nambu-Goldstone boson associated with axial symmetry breaking.

Abstract

Spontaneous symmetry breaking is studied within a simple version of the light-front sigma model with fermions. Its vacuum structure is derived by an implementation of global symmetries in terms of unitary operators in a finite volume with periodic fermi field. Due to the dynamical fermion zero mode, the vector and axial U(1) charges do not annihilate the light-front vacuum. The latter is transformed into a continuous set of degenerate vacuum states, leading to to the spontaneous breakdown of the axial symmetry. The existence of associated massless Nambu-Goldstone boson is demonstrated.