N=2 four-dimensional gauge theories from fractional branes

TL;DR

This work analyzes 4D $N=2$ gauge theories realized on fractional D3-branes at a $R^{1,5}\times R^4/Z_2$ orbifold. By constructing the full classical supergravity solution, it shows that gravity captures the perturbative moduli space and beta-functions but not nonperturbative instanton effects, which are associated with the enhançon mechanism and require additional string degrees of freedom. The authors establish a wrapped-brane interpretation via the McKay correspondence, relate twisted fluxes to gauge couplings, and demonstrate a precise gravity–gauge dictionary through probe analysis, including the Seiberg-Witten perturbative structure. They conclude that while supergravity encodes the perturbative regime and provides valuable insights into the gauge dynamics, accessing the full nonperturbative content demands incorporating stringy phenomena such as fractional D-instantons.

Abstract

This is a pedagogical and extended version of the results published in Refs. [1,2] and presented by the authors in various talks during the last year. We discuss the type II D-branes (both regular and fractional) of the orbifold R^{1,5}*R^4/Z_2, we determine their corresponding supergravity solution and show how this can be used to study the properties of N=2 super Yang-Mills. Supergravity is able to reproduce the perturbative moduli space of the gauge theory, while it does not encode the non-perturbative corrections. The short distance region of space-time, which corresponds to the infrared region of the gauge theory, is excised by an enhancon mechanism, and more states should be included in the low energy effective action in order to enter inside the enhancon and recover the instanton corrections. (To be published on a Memorial Volume commemorating Michael Marinov)