Spontaneous Symmetry Breaking and Proper-Time Flow Equations

TL;DR

This paper explores spontaneous symmetry breaking using non-perturbative renormalization group flow equations with proper-time regularization, demonstrating convexity of the potential and validating results with lattice simulations.

Contribution

It introduces a novel approach employing proper-time flow equations to study symmetry breaking, combining analytical, numerical, and Monte Carlo methods for validation.

Findings

Convexity of the local potential is achieved through the flow equations.

Good agreement between lattice simulations and RG solutions in various regimes.

The method effectively captures both strong and weak coupling behaviors.

Abstract

We discuss the phenomenon of spontaneous symmetry breaking by means of a class of non-perturbative renormalization group flow equations which employ a regulating smearing function in the proper-time integration. We show, both analytically and numerically, that the convexity property of the renormalized local potential is obtained by means of the integration of arbitrarily low momenta in the flow equation. Hybrid Monte Carlo simulations are performed to compare the lattice Effective Potential with the numerical solution of the renormalization group flow equation. We find very good agreement both in the strong and in the weak coupling regime.