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

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.

24 pages, 18 figures. Added references and minor rewordings: published version

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Cited by in corpus (18)

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• Functional renormalization group and 2PI effective action formalism
• The 2PI effective action at four loop order in ${\phi }^4$ theory
• Renormalized Linear Kinetic Theory as Derived from Quantum Field Theory - a novel diagrammatic method for computing transport coefficients -
• Broken phase scalar effective potential and Phi-derivable approximations
• Renormalization group flow equations connected to the $n$PI effective action
• Bethe-Salpeter Equations from the 4PI effective action
• Transport coefficients of O(N) scalar field theories close to the critical point
• 4-point vertices from the 2PI and 4PI Effective Actions
• A new method to calculate the n-Particle Irreducible Effective Action
• Renormalization of the 4PI effective action using the functional renormalization group
• Decoherence in an Interacting Quantum Field Theory: Thermal Case
• On the contribution of plasminos to the shear viscosity of a hot and dense Yukawa-Fermi gas
• Results from the 4PI Effective Action in 2- and 3-dimensions
• 2PI Effective Action and Evolution Equations of N = 4 super Yang-Mills