N=1 Super Yang Mills renormalization schemes for Fractional Branes

TL;DR

This paper explores how different renormalization schemes in N=1 super Yang-Mills theory relate to supergravity descriptions, revealing scheme independence and establishing a new relation between gaugino condensate and supergravity coordinates.

Contribution

It introduces a framework for understanding renormalization schemes in supergravity duals of N=1 SYM and derives a novel relation involving gaugino condensate.

Findings

No privileged renormalization scheme linked to a specific supergravity solution.

Explicit comparison of Wilsonian and multi-loop schemes.

New functional relation between gaugino condensate and supergravity coordinates.

Abstract

We investigate N=1 super Yang-Mills theory using fractional branes. We first define the beta-function with respect to a supergravity coordinate. To provide the relation between the supergravity parameter and the renormalization group scale we use the UV known gauge theory beta-function as a type of boundary condition. We show that there are no privileged renormalization schemes connected to a given supergravity solution while we investigate in some detail two schemes. The Wilsonian one where just one loop is manifest and the one containing multi-loops. A new functional relation between the gaugino condensate and the supergravity coordinates is finally determined.