Symmetry Improved CJT Effective Action

TL;DR

This paper introduces a symmetry-improved CJT formalism that enforces global symmetries in non-perturbative quantum thermal field theory, ensuring massless Goldstone bosons and correct phase transition behavior.

Contribution

The authors develop a novel symmetry-improved CJT approach that incorporates Ward identities, resolving residual symmetry violations in the standard formalism.

Findings

Goldstone boson remains massless in the broken phase

Phase transition is second order in the improved formalism

Proper threshold behavior of Goldstone and Higgs particles is achieved

Abstract

The formalism introduced by Cornwall, Jackiw and Tomboulis (CJT) provides a systematic approach to consistently resumming non-perturbative effects in Quantum Thermal Field Theory. One major limitation of the CJT effective action is that its loopwise expansion introduces residual violations of possible global symmetries, thus giving rise to massive Goldstone bosons in the spontaneously broken phase of the theory. In this paper we develop a novel symmetry-improved CJT formalism for consistently encoding global symmetries in a loopwise expansion. In our formalism, the extremal solutions of the fields and propagators to a loopwise truncated CJT effective action are subject to additional constraints given by the Ward identities due to global symmetries. By considering a simple O(2) scalar model, we show that, unlike other methods, our approach satisfies a number of important field-theoretic properties. In particular, we find that the Goldstone boson resulting from spontaneous symmetry breaking of O(2) is massless and the phase transition is a second order one, already in the Hartree-Fock approximation. After taking the sunset diagrams into account, we show how our approach properly describes the threshold properties of the massless Goldstone boson and the Higgs particle in the loops. Finally, assuming minimal modifications to the Hartree-Fock approximated CJT effective action, we calculate the corresponding symmetry-improved CJT effective potential and discuss the conditions for its uniqueness for scalar-field values away from its minimum.