Dimensional Reduction, Hard Thermal Loops and the Renormalization Group

TL;DR

This paper investigates the applicability of dimensional reduction and hard thermal loop expansion in finite-temperature lambda phi^4 theory using a finite-temperature renormalization group, revealing conditions under which these approximations hold near phase transitions.

Contribution

It introduces a finite-temperature renormalization group approach to analyze the validity of dimensional reduction and HTL expansion across temperature regimes.

Findings

Dimensional reduction applies at high temperatures for small coupling constants.

HTL expansion is valid below and away from the phase transition at high temperatures.

Near the critical temperature, thermal fluctuations dominate and are not captured by HTL.

Abstract

We study the realization of dimensional reduction and the validity of the hard thermal loop expansion for lambda phi^4 theory at finite temperature, using an environmentally friendly finite-temperature renormalization group with a fiducial temperature as flow parameter. The one-loop renormalization group allows for a consistent description of the system at low and high temperatures, and in particular of the phase transition. The main results are that dimensional reduction applies, apart from a range of temperatures around the phase transition, at high temperatures (compared to the zero temperature mass) only for sufficiently small coupling constants, while the HTL expansion is valid below (and rather far from) the phase transition, and, again, at high temperatures only in the case of sufficiently small coupling constants. We emphasize that close to the critical temperature, physics is completely dominated by thermal fluctuations that are not resummed in the hard thermal loop approach and where universal quantities are independent of the parameters of the fundamental four-dimensional theory.