Non-perturbative renormalization for lattice massive QED2: the ultraviolet problem

Abstract: I will consider a lattice regularization of the massive QED in 2d, describing a Dirac fermion interacting with a massive vector field, in the regime in which the fermion mass is much smaller than the boson mass and the latter is much smaller than the ultraviolet cut-off, which is the suitable one to mimic a realistic 4d massive gauge theory like the Electroweak sector. The presence of the lattice and of non-zero fermion mass breaks any solvability property. I will show that the effective action obtained after the integration of the ultraviolet degrees of freedom is expressed by expansions which are convergent for values of the coupling (electric charge) independent on the fermion mass and the ultraviolet cut-off, and with cut-off-independent bare parameters. By combining this result with the analysis of the infrared part in previous papers we get a complete construction of the model and a number of properties whose analogous are expected to hold in 4d. As I will discuss, the choice of lattice rather than momentum regularization, essential for ensuring Ward Identities, requires the development of new methods to get the necessary non-perturbative bounds. Based on a recent joint work with V. Mastropietro (Roma La Sapienza) and B. Renzi (SISSA).

MathematicsPhysics

Audience: researchers in the topic

Probability, Statistical Mechanics and Quantum Fields

Series comments: Paweł Duch (EPFL) will give a mini-course on "Singular Stochastic PDEs", in the period March 9-20, 2026. Further information can be found here: www.math.sissa.it/course/phd-course/singular-stochastic-pdes. You can follow the course online here: sissa-it.zoom.us/j/84337146226?pwd=SMrOupIjXvQ2pwrc6djLExOCKZPbKZ.1. Please email Ilya Chevyrev for the Zoom passcode.