Pedagogical comments about nonperturbative Ward-constrained melonic renormalization group flow
Résumé
This paper, in addition to our recent works, intends to improve and give in detail the behavior of the Wetterich flow equations in the physical theory space. We focus on the local potential approximation and present a new framework of investigation, namely the effective vertex expansion coupled with Ward’s identities for quartic melonic interactions, allowing us to consider infinite sectors rather than finite dimensional subspaces of the full theory space. The flow behavior in the vicinity of the Gaussian fixed point and the correction given by the effective vertex expansion is also analyzed. The dynamical constrained flow allows us to identify the influence of the number of melonic interactions related to the existence of divergence at which the possible first order phase transition may be identified is studied. Comparing our results using the formalism of Callan Symanzik equation is also scrutinized.