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… Click to show full 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.
               
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