A Soluble Model of Four-Fermion Interactions in de Sitter Space

TL;DR

This paper analyzes four-fermion interactions in de Sitter space, deriving an effective potential and identifying a critical curvature where fermion mass vanishes, revealing how space-time curvature influences fermion dynamics.

Contribution

It provides an analytical calculation of the effective potential and critical curvature for four-fermion interactions in de Sitter space using a 1/N expansion.

Findings

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

Critical curvature at which fermion mass vanishes is analytically determined.

Fermion mass depends on space-time curvature.

Abstract

We consider the theory of four-fermion interactions with N-component fermions in de Sitter space. It is found that the effective potential for a composite operator in the theory is calculable in the leading order of the 1/N expansion. The resulting effective potential is analyzed by varying both the four-fermion coupling constant and the curvature of the space-time. The critical curvature at which the dynamically generated fermion mass disappears is found to exist and is calculated analytically. The dynamical fermion mass is expressed as a function of the space-time curvature.