Dimensional Reduction, Hard Thermal Loops and the Renormalization Group

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.

20 pages, 13 eps figures, uses epsfig and pstricks

References in corpus (17)

• Is There a Hot Electroweak Phase Transition at $m_H\gsim m_W$?
• The Electroweak Phase Transition: A Non-Perturbative Analysis
• Generic Rules for High Temperature Dimensional Reduction and Their Application to the Standard Model
• Resummation in a Hot Scalar Field Theory
• 3D Physics and the Electroweak Phase Transition: Perturbation Theory
• A Non-Perturbative Analysis of the Finite T Phase Transition in SU(2)xU(1) Electroweak Theory
• The universality class of the electroweak theory
• A Lattice Monte Carlo Study of the Hot Electroweak Phase Transition
• The Electroweak Phase Transition at $m_H\simeq m_W$
• Three-dimensional U(1) gauge+Higgs theory as an effective theory for finite temperature phase transitions
• Effective Critical Exponents for Dimensional Ccrossover and Quantum Systems from an Environmentally Friendly Renormalization Group
• Environmentally Friendly Renormalization
• Critical Behavior in the Electroweak Phase Transition
• The renormalized gauge coupling and non-perturbative tests of dimensional reduction
• Comparison of 4d and 3d Lattice Results for the Electroweak Phase Transition
• Critical Temperature and Amplitude Ratios from a Finite-Temperature Renormalization Group
• The Specific Heat of a Ferromagnetic Film.