Next-to-Leading Order Transport Coefficients from the Four-Particle Irreducible Effective Action

TL;DR

This paper develops a framework using the 4PI effective action to compute next-to-leading order transport coefficients, such as shear viscosity, in scalar field theories with spontaneous symmetry breaking.

Contribution

It extends the 3PI formalism to 4PI at four loops, deriving integral equations for the 2-point function to calculate NLO transport coefficients.

Findings

Derived integral equations for 2-point functions at 4-loop 4PI level.

Framework enables calculation of NLO contributions to shear viscosity.

Provides a natural, resummation-based approach for transport coefficient computation.

Abstract

Transport coefficients can be obtained from 2-point correlators using the Kubo formulae. It has been shown that the full leading order result for electrical conductivity and (QCD) shear viscosity is contained in the re-summed 2-point function that is obtained from the 3-loop 3PI re-summed effective action. The theory produces all leading order contributions without the necessity for power counting, and in this sense it provides a natural framework for the calculation. In this article we study the 4-loop 4PI effective action for a scalar theory with cubic and quartic interactions in the presence of spontaneous symmetry breaking. We obtain a set of integral equations that determine the re-summed 2-point vertex function. A next-to-leading order contribution to the viscosity could be obtained from this set of coupled equations.