On the geometry and the moduli space of β-deformed quiver gauge theories

Abstract

We consider a class of super-conformal β-deformed = 1 gauge theories dual to string theory on AdS 5 × X with fluxes, where X is a deformed Sasaki-Einstein manifold. The supergravity backgrounds are explicit examples of Generalised Calabi-Yau manifolds: the cone over X admits an integrable generalised complex structure in terms of which the BPS sector of the gauge theory can be described. The moduli spaces of the deformed toric = 1 gauge theories are studied on a number of examples and are in agreement with the moduli spaces of D3 and D5 static and dual giant probes.