Dynamical Symmetry Breaking in Einstein Universe

TL;DR

This paper studies how space-time curvature in Einstein universe influences dynamical symmetry breaking of four-fermion interactions, revealing a second-order phase transition and analytically determining the critical curvature for symmetry restoration.

Contribution

It provides an analytical calculation of the effective potential and critical curvature for symmetry restoration in four-fermion interactions in Einstein universe across various dimensions.

Findings

Symmetry is restored via a second-order phase transition as curvature increases.

The critical curvature for fermion mass disappearance is analytically derived.

Effective potential is calculable in the leading order of 1/N expansion.

Abstract

We investigate four-fermion interactions with $N$-component fermion in Einstein universe for arbitrary space-time dimensions ($2 \leq D<4$). It is found that the effective potential for composite operator $\overline{\psi}\psi$ is calculable in the leading order of the $1/N$ expansion. The resulting effective potential is analyzed by varying the curvature of the space-time and is found to exhibit the symmetry restoration through the second-order phase transition. The critical curvature at which the dynamical fermion mass disappears is analytically calculated.