Gravity duals to deformed SYM theories and Generalized Complex Geometry

TL;DR

This work develops a generalized complex geometry approach to classify and construct Type IIB gravity duals of mass and beta deformations of four-dimensional conformal field theories. By focusing on SU(2) structure backgrounds, it identifies a conformally closed vector $z$ and a closed modified two-form $\hat{J}$ as the central geometric data, with the vector encoding the deformation type through the superpotential. The Pilch-Warner mass-flow and Lunin-Maldacena beta-deformation are shown to belong to this class, and a simple, generalized Kahler-potential framework yields AdS5 solutions whose fluxes are fixed by the potential. The analysis also details how T-duality generates marginal deformations and analyzes D3-brane probe moduli, providing a path to uncover new warped AdS5 backgrounds with fluxes and their dual gauge theories.

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.