Wilsonian renormalisation group and thermal field theory in the Schwinger-Keldysh closed-time-path formalism

TL;DR

This paper applies Wilsonian renormalisation group techniques to finite-temperature scalar field theory within the Schwinger-Keldysh formalism, revealing new fixed points and effective interactions relevant for understanding thermal quantum fields.

Contribution

It provides a microscopic derivation of effective CTP actions at finite temperature and identifies two novel fixed points in the RG flow in four dimensions.

Findings

Existence of two new fixed points in 4D RG flow.

Derivation of effective interactions coupling CTP branches.

Relation of one fixed point to Wilson-Fisher fixed point.

Abstract

We study perturbative Wilsonian renormalisation group (RG) for the scalar $\phi^4$ theory at finite temperature to one loop order in the Schwinger-Keldysh closed-time-path (CTP) formalism. By explicitly integrating out the UV modes, we show how effective interactions coupling the two branches of the CTP contour arise. This provides a microscopic derivation of the type of effective CTP actions used in the literature. While the full effective theory has no critical points, we instead proceed to study critical properties of the RG flow in a reduced space of complex couplings that characterise certain time-ordered correlators and show the existence of two novel fixed points in $d=4$ spacetime dimensions. We relate one to the Wilson-Fisher fixed point known to exist only in $4-\epsilon$ dimensions, and the other to the standard Gaussian fixed point.