Fractional D-branes and their gauge duals

TL;DR

This paper explores the supergravity dual of fractional D3-branes on R^4/Z_2, revealing a singularity that is resolved by an enhancon mechanism and demonstrating a logarithmic coupling running matching N=2 super Yang-Mills theory.

Contribution

It provides a detailed classical supergravity solution for fractional D3-branes and connects the geometry to the gauge theory's coupling and beta-function.

Findings

Identification of the gauge coupling in terms of string parameters

Resolution of the supergravity singularity via the enhancon mechanism

Matching the supergravity running coupling with the gauge theory beta-function

Abstract

We study the classical geometry associated to fractional D3-branes of type IIB string theory on R^4/Z_2 which provide the gravitational dual for N=2 super Yang-Mills theory in four dimensions. As one can expect from the lack of conformal invariance on the gauge theory side, the gravitational background displays a repulson-like singularity. It turns out however, that such singularity can be excised by an enhancon mechanism. The complete knowledge of the classical supergravity solution allows us to identify the coupling constant of the dual gauge theory in terms of the string parameters and to find a logarithmic running that is governed precisely by the beta-function of the N=2 super Yang-Mills theory.