Linear Response Theory for Symmetry Improved Two Particle Irreducible Effective Actions

Abstract

We investigate the linear response of an O(N) scalar quantum field theory subject to external perturbations using the symmetry improved two particle irreducible effective action formalism [A. Pilaftsis and D. Teresi, Nucl. Phys. B874, 594 (2013)]. Despite satisfactory equilibrium behavior, we find a number of unphysical effects at the linear response level. Goldstone boson field fluctuations are over-determined, with the only consistent solution being to set the fluctuations and their driving sources to zero, except for momentum modes where the Higgs and Goldstone self-energies obey a particular relationship. Also Higgs field fluctuations propagate masslessly, despite the Higgs propagator having the correct mass. These pathologies are independent of any truncation of the effective action and still exist even if we relax the over-determining Ward identities, so long as the constraint is formulated O(N)-covariantly. We discuss possible reasons for the apparent incompatibility of the constraints and linear response approximation and possible ways forward.

arXiv comment13 pages, 0 figures, REVTeX 4.1, amsmath. Minor fixes and added discussion strengthening our conclusions

References in corpus (10)

• Quantum Field Theory in the Large N Limit: a review
• Introduction to Nonequilibrium Quantum Field Theory
• Symmetry Improved CJT Effective Action
• Constraining the effective action by a method of external sources
• Symmetry-Improved 2PI Approach to the Goldstone-Boson IR Problem of the SM Effective Potential
• Symmetry Improved 2PI Effective Action and the Infrared Divergences of the Standard Model
• On the symmetry improved CJT formalism in the $O(4)$ linear sigma model
• Symmetry improvement of 3PI effective actions for O(N) scalar field theory
• Two-particle irreducible effective actions versus resummation: analytic properties and self-consistency
• Pion String evolving in a thermal bath

Cited by in corpus (5)

• The 2PI effective theory at next-to-leading order using the functional renormalization group
• Exact RG Invariance and Symmetry Improved 2PI Effective Potential
• Loss of solution in the symmetry improved Phi-derivable expansion scheme
• Renormalization of the 4PI effective action using the functional renormalization group
• Soft symmetry improvement of two particle irreducible effective actions