On the CJT Formalism in Multi-Field Theories

TL;DR

This paper examines the application of the CJT formalism in multi-field theories, focusing on temperature effects and ultraviolet issues, and demonstrates its consistency in a two-scalar-field model relevant for symmetry nonrestoration at high temperatures.

Contribution

It analyzes the CJT formalism's issues in multi-field theories and confirms its validity at lowest order for a two-scalar-field model related to symmetry nonrestoration.

Findings

CJT formalism issues in multi-field theories are identified.

Lowest order approximation yields consistent results.

Results support studies on symmetry nonrestoration at high temperatures.

Abstract

The issues that arise when using the Cornwall-Jackiw-Tomboulis formalism in multi-field theories are investigated. Particular attention is devoted to the interplay between temperature effects, ultraviolet structure, and the interdependence of the gap equations. Results are presented explicitly in the case of the evaluation of the finite temperature effective potential of a theory with two scalar fields which has attracted interest as a toy model for symmetry nonrestoration at high temperatures. The lowest nontrivial order of approximation of the Cornwall-Jackiw-Tomboulis effective potential is shown to lead to consistent results, which are relevant for recent studies of symmetry nonrestoration by Bimonte and Lozano.