Fractional D-branes and their gauge duals

TL;DR

This paper constructs the gravity dual for fractional D3-branes on ${\rm IR}^{1,5}\times{\rm IR}^{4}/{\bf Z}_2$ and shows that the corresponding ${U}(M)$ ${\cal N}=2$ SYM theory is non-conformal, with a repulson-type singularity resolved by an enhançon mechanism. Using boundary-state methods, it derives the full classical solution, including both untwisted and twisted sectors, and demonstrates a no-force BPS configuration. The warp factor and twisted fields yield a logarithmic running of the gauge coupling that precisely reproduces the ${\cal N}=2$ beta-function, identifying the YM coupling in terms of string parameters and linking the RR twisted scalar to the theta angle. These results establish a concrete gauge/gravity dictionary for a non-conformal, less supersymmetric theory and highlight how stringy effects encoded in the enhançon capture non-perturbative field theory information.

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.