Finite temperature field theory and phase transitions

TL;DR

The work articulates a detailed framework for zero- and finite-temperature field theory and its application to cosmological phase transitions and baryogenesis. It develops the effective potential at both $T=0$ and finite $T$, contrasts renormalization schemes, and presents RG-improved forms; it then analyzes cosmological phase transitions, including bubble nucleation and thermal tunneling, before addressing baryogenesis through electroweak processes. A central finding is that the Standard Model, with current Higgs constraints, cannot sustain a strong enough first-order transition to preserve any generated baryon asymmetry, whereas MSSM settings with light stops and CP-violating phases can realize viable electroweak baryogenesis under certain parameter ranges. The discussion highlights the interplay between perturbative limits, resummation, and nonperturbative effects (sphalerons) in shaping early universe dynamics and observable consequences.

Abstract

We review different aspects of field theory at zero and finite temperature, related to the theory of phase transitions. We discuss different renormalization conditions for the effective potential at zero temperature, emphasizing in particular the MS-bar renormalization scheme. Finite temperature field theory is discussed in the real and imaginary time formalisms, showing their equivalence in simple examples. Bubble nucleation by thermal tunneling, and the subsequent development of the phase transition is described in some detail. Some attention is also devoted to the breakdown of the perturbative expansion and the infrared problem in the finite temperature field theory. Finally the application to baryogenesis at the electroweak phase transition is done in the Standard Model and in the Minimal Supersymmetric Standard Model. In all cases we have translated the condition of not washing out any previously generated baryon asymmetry by upper bounds on the Higgs mass.

Figures (9)

• Figure 1: 1PI diagrams contributing to the one-loop effective potential of (\ref{['scallag']}).
• Figure 2: 1PI diagrams contributing to the one-loop effective potential of (\ref{['fermlag']}).
• Figure 3: 1PI diagrams contributing to the one-loop effective potential of (\ref{['gaugelag']}).
• Figure 4: Contour used in the real time formalism.
• Figure 5: One-loop contribution to the self-energy for the scalar theory.