Higher Derivative Four-Fermion Model in Curved Spacetime

TL;DR

This paper investigates how curvature influences phase transitions and mass generation in a higher derivative four-fermion model in four-dimensional curved spacetime, revealing curvature-induced symmetry breaking phenomena.

Contribution

It introduces a detailed analysis of the phase structure and dynamical mass generation in a higher derivative four-fermion model within curved spacetime, using the $1/N_c$-expansion and local momentum representation.

Findings

Curvature induces symmetry breaking and phase transitions.

Dynamically generated fermionic mass depends on curvature and coupling.

Effective potential evaluated in linear curvature approximation.

Abstract

We discuss the phase structure of a higher derivative four-fermion model in four dimensions in curved spacetime in frames of the $\frac{1}{N_c}$-expansion. First, we evaluate in our model the effective potential of two composite scalars in the linear curvature approximation using a local momentum representation in curved spacetime for the higher-derivative propagator which naturally appears. The symmetry breaking phenomenon and phase transition induced by curvature are numerically investigated. A numerical study of the dynamically generated fermionic mass, which depends on the coupling constants and on the curvature, is also presented.