The beta function of N=1 SYM in Differential Renormalization

TL;DR

This paper computes the two-loop beta function of N=1 SYM using differential renormalization, clarifying the relation between ultraviolet renormalization and the renormalization group flow.

Contribution

It provides a complete two-loop calculation of the beta function in N=1 SYM using differential renormalization, linking UV renormalization to the Wilsonian coupling flow.

Findings

Two-loop beta function obtained in position and momentum space.

Ultraviolet divergences renormalized in position space.

Infrared divergences handled in momentum space.

Abstract

Using differential renormalization, we calculate the complete two-point function of the background gauge superfield in pure N=1 Supersymmetric Yang-Mills theory to two loops. Ultraviolet and (off-shell) infrared divergences are renormalized in position and momentum space respectively. This allows us to reobtain the beta function from the dependence on the ultraviolet renormalization scale in an infrared-safe way. The two-loop coefficient of the beta function is generated by the one-loop ultraviolet renormalization of the quantum gauge field via nonlocal terms which are infrared divergent on shell. We also discuss the connection of the beta function to the flow of the Wilsonian coupling.