Dimensionally reduced U(1)+Higgs theory in the broken phase

TL;DR

The paper tackles the validity of dimensional reduction from finite-temperature 4d U(1)+Higgs theory to a 3d effective theory in the broken phase. It combines analytic perturbative calculations up to 3 loops (with Coleman-Weinberg optimization) with nonperturbative lattice Monte Carlo simulations to study the scalar condensate and propagators. The main finding is that CW-optimized 2-loop perturbation accurately reproduces the condensate data across a range up to near $T_c$, while the scalar correlator exhibits a persistent ~25% discrepancy, underscoring the need for higher-loop results for the scalar propagator in gauge theories. Overall, the work validates the 3d reduced theory as a viable framework for finite-temperature gauge-Higgs dynamics and highlights where perturbation theory remains reliable and where it does not.

Abstract

We apply dimensional reduction to the finite temperature U(1)+Higgs theory and study the properties of the reduced 3-dimensional theory in the broken phase using lattice Monte Carlo simulations. We compute analytically the scalar condensate in optimized 2-loop perturbation theory and the correlators in 1-loop perturbation theory. These quantities are also calculated numerically. The two results for the condensate agree well but a 25\% difference is observed for the scalar correlator, indicating the need for optimized 2-loop perturbative results.

Figures (13)

• Figure 1: The 2-loop diagrams contributing to the 3d effective potential.
• Figure 2: The renormalization group improved 2-loop potential near the phase transition point, with $m_H=35$ GeV.
• Figure 3: The 2-loop potential with $m_H=60$ GeV.
• Figure 4: Fitted $\kappa(\phi)$:s with $m_H=35$ GeV, $T=148.83$ GeV $\approx T_c$ and $m_H=60$ GeV, $T=226.77$ GeV $\approx T_c$.
• Figure 5: The 1-loop diagrams contributing to the scalar propagator.