Holographic renormalization group flow, Wilson loops and field-theory beta-functions

TL;DR

This paper investigates the RG flow of string theory backgrounds, analyzing beta-functions and Wilson loops in theories with different IR behaviors, including confinement and conformal fixed points.

Contribution

It introduces a framework for studying RG flows in string theory backgrounds with diverse IR properties, including beta-function poles and confinement regimes.

Findings

Identified the range of couplings leading to confinement in certain theories.

Calculated Wilson loops for theories with IR poles in beta-functions.

Analyzed the relation between conformal fixed points and beta-function poles.

Abstract

We study the Renormalization Group (RG) flow of critical bosonic background fields in the framework of the RG approach to string theory. In this approach quantum field theory beta-functions are the extra inputs in solving the string theory sigma-model equations. We study two different situations, the first one is the Yang-Mills theory where the coupling constant diverges in the infrared limit. The second case corresponds to a type of theories where the beta-function has a pole in the infrared limit and it changes sign through the pole (as in N=1 super-Yang-Mills theory). For this case in the strong coupling branch, in the infrared, there is an interval of values of the coupling in which the theory only leads to confinement. We have obtained this range. We also mention the theories with conformal-fixed points and their relation to theories with a pole in the beta-functions. We calculate the Wilson loops in these theories.