Gravity duals to deformed SYM theories and Generalized Complex Geometry

TL;DR

This paper investigates specific supersymmetric backgrounds in Type IIB supergravity relevant for the AdS/CFT correspondence, revealing geometric structures that encode gauge theory deformations like mass and beta-deformations.

Contribution

It characterizes a class of SU(2) structure backgrounds using Generalized Complex Geometry, linking geometric features to gauge theory deformations and including known solutions as special cases.

Findings

Identified geometric conditions for supersymmetric backgrounds with SU(2) structure.

Connected geometric features to superpotential and deformation types.

Included known solutions like Pilch-Warner and Lunin-Maldacena within this class.

Abstract

We analyze the supersymmetry conditions for a class of SU(2) structure backgrounds of Type IIB supergravity, corresponding to a specific ansatz for the supersymmetry parameters. These backgrounds are relevant for the AdS/CFT correspondence since they are suitable to describe mass deformations or beta-deformations of four-dimensional superconformal gauge theories. Using Generalized Complex Geometry we show that these geometries are characterized by a closed nowhere-vanishing vector field and a modified fundamental form which is also closed. The vector field encodes the information about the superpotential and the type of deformation - mass or beta respectively. We also show that the Pilch-Warner solution dual to a mass-deformation of N =4 Super Yang-Mills and the Lunin-Maldacena beta-deformation of the same background fall in our class of solutions.