Conformal Manifolds for the Conifold and other Toric Field Theories

TL;DR

This paper identifies the conformal manifolds of 4D N=1 gauge theories associated with D3 branes probing toric Calabi-Yau singularities, including the conifold, and explores their exactly marginal deformations.

Contribution

It explicitly determines the conformal manifolds for all Y^{p,q} toric singularities, highlighting the dimensionality and the existence of a universal beta-deformation.

Findings

Conformal manifold for Y^{p,q} is three-dimensional.

Conformal manifold for the conifold (Y^{1,0}) is five-dimensional.

A universal beta-deformation exists for all toric Calabi-Yau singularities.

Abstract

In the space of couplings of the 4D N=1 gauge theory associated to D3 branes probing Calabi-Yau singularities, there is a manifold over which superconformal invariance is preserved. The AdS/CFT correspondence is valid precisely for this "conformal manifold". We identify the conformal manifold for all the Y^{p,q} toric singularities, paying special attention to the case of the conifold, Y^{1,0}. For a general Y^{p,q} the conformal manifold is three dimensional, while for the conifold it is five dimensional. There is always an exactly marginal deformation, analogous to the beta-deformation of N=4 SYM, which involves fluxes in the dual gravity description. This beta-deformation exists for any toric Calabi-Yau singularity.