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

TL;DR

This paper explores the geometric structure and moduli spaces of beta-deformed superconformal N=1 gauge theories, revealing their connection to generalized Calabi-Yau manifolds and matching gauge theory moduli with probe brane results.

Contribution

It provides explicit supergravity backgrounds for beta-deformed theories and analyzes their moduli spaces, linking gauge theory deformations to geometric structures.

Findings

Moduli spaces match D3 and D5 probe results.

Supergravity backgrounds are explicit examples of Generalised Calabi-Yau manifolds.

The cone over the deformed manifold admits an integrable generalized complex structure.

Abstract

We consider a class of super-conformal beta-deformed N=1 gauge theories dual to string theory on $AdS_5 \times X$ 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 N=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.