Fractional Branes and N=1 Gauge Theories

TL;DR

This paper explores fractional D3-branes on a specific orbifold, analyzing their spectra, gauge theories, and supergravity solutions, and derives the beta-function for certain N=1 gauge theories using probe techniques.

Contribution

It provides a detailed study of fractional branes on C^3/Z_2*Z_2, including spectra, supergravity solutions, and beta-function calculations for N=1 gauge theories.

Findings

Derived the supergravity solution for fractional branes.

Obtained the Wilsonian beta-function for N=1 theories with chiral multiplets.

Proposed a method to infer beta-functions for pure N=1 Yang-Mills.

Abstract

We discuss fractional D3-branes on the orbifold C^3/Z_2*Z_2. We study the open and the closed string spectrum on this orbifold. The corresponding N=1 theory on the brane has, generically, a U(N_1)*U(N_2)*U(N_3)*U(N_4) gauge group with matter in the bifundamental. In particular, when only one type of brane is present, one obtains pure N=1 Yang-Mills. We study the coupling of the branes to the bulk fields and present the corresponding supergravity solution, valid at large distances. By using a probe analysis, we are able to obtain the Wilsonian beta-function for those gauge theories that possess some chiral multiplet. Although, due to the lack of moduli, the probe technique is not directly applicable to the case of pure N=1 Yang-Mills, we point out that the same formula gives the correct result also for this case.