Stochastic dynamics for Group Field Theories

TL;DR

This paper investigates phase transitions in group field theories by modeling their dynamics with stochastic processes and Langevin equations, focusing on a complex Abelian model of rank 5 and analyzing its properties through renormalization group techniques.

Contribution

It introduces a stochastic dynamics framework for group field theories using Langevin equations and studies their properties via renormalization group analysis.

Findings

Identification of ergodicity breaking in the model

Analysis of phase transition behavior in the tensor field

Insights into the renormalization group flow of the stochastic model

Abstract

Phase transitions with spontaneous symmetry breaking are expected for group field theories as a basic feature of the geometogenesis scenario. The following paper aims to investigate the equilibrium phase for group field theory by using the ergodic hypothesis on which the Gibbs-Boltzmann distributions must break down. The breaking of the ergodicity can be considered dynamically, by introducing a fictitious time inducing a stochastic process described through a Langevin equation, from which the randomness of the tensor field will be a consequence. This type of equation is considered particularly for complex just-renormalizable Abelian model of rank d = 5, and we study some of their properties by using a renormalization group considering a coarse-graining both in time and space.