Renormalization at all orders for lattice infrared QED4 with massless electron

One of the goals of constructive Quantum Field Theory (QFT) is to provide a convergent algorithm for computing a consistent set of Euclidean correlation functions starting from a given bare action and, next, to reconstruct the corresponding real-time correlations via analytic continuation in the time variable. This program proved successful for constructing several low dimensional toy QFT models but results in 3 and 4 dimensions are still scarce. Until now, not even a consistent construction of infrared QED4 with small electron mass at all orders in renormalized perturbation theory was available, unless a loop regularization scheme was employed or a number of non-gauge-invariant counter-terms were included in the bare action.

In this talk I will describe such a consistent construction, at all orders in renormalized perturbation theory, in a lattice gauge theory model of QED4 with massless electron and no other counter-term than the one for the electron mass. We also prove that, in the presence of an infrared (IR) cutoff on the photon propagator, the model is non-perturbatively well-defined, provided the electron charge is sufficiently small (a priori, non-uniformly in the IR cutoff).

The proof is based on a Wilsonian Renormalization Group (RG) scheme and uses ideas developed in the last decade in the context of lattice gauge theory models of graphene and Weyl semimetals. In particular, we use Ward Identities at each RG step to control the flow of the effective couplings, including the non-gauge-invariant ones produced at intermediate steps by the multiscale procedure, and prove their infrared asymptotic freedom. Time permitting, I will comment on the perspectives opened by this and related works on the full construction of infrared QED4, on the non-perturbative computation of the chiral anomaly and on the spontaneous emergence of Lorentz symmetry. Joint work with Marco Falconi and Vieri Mastropietro.