Seminari del Dipartimento

Fisica Matematica

The problem of perturbative renormalization of phi^4 and Yang-Mills theories is studied in four dimensional Euclidean space. The analysis is based on the Functional Renormalization group. This is a unified approach which permits to study a large class of field theories without recourse to Feynman diagrams. An important part of the work consists in establishing upper bounds in momentum space on all vertex functions at all loop orders. These bounds have a very natural graphical interpretation in form of trees. In Yang-Mills theory introduction of ultraviolet(UV) and infrared(IR) cut-offs breaks BRST invariance. Thus it is essential to prove at all loop orders that the construction can be accomplished in such a way that BRST invariance is restored when the UV cut-off goes to infinity. As a useful application we derive the violated Slavnov–Taylor identities for the effective action in the Maximal Abelian Gauge and show the existence of the gluon condensate in the effective low energy theory obtained in one loop. We also consider the renormalization of the stochastic singular PDE for the Gross-Neveu-Yukawa interaction in two dimensional Euclidean space using the theory of regularity structures.
 
org: GIULIANI Alessandro