Generalized Geometry and Hopf Twists

Abstract

The Leigh-Strassler theories are marginal deformations of the N = 4 SYM theory preserving N = 1 Supersymmetry. As such they admit a Hopf algebra structure which is a quantum group deformation of the SU(3) structure of the R-symmetry of N = 4 SYM. We reproduce the b-deformed theory, a subset of the Leigh-Strassler theories, from the Hopf twist approach and investigate how the twist manifests itself on the gravity dual by defining a star product between chiral superfields of the b-deformed field theory. The treatment on the gravity side is done in the Generalized Geometry framework. This star product is then used to deform the pure spinors of six-dimensional flat space and from the deformed spinors we obtain an N = 2 solution of Supergravity. The Lunin-Maldacena background dual to the b-deformed theory is recovered when a stack of D3-branes is introduced in this N = 2 solution. Alongside the b-deformed theory we consider a unitarily equivalent theory, which we refer to as a wdeformed theory. In this approach the role of the twist is transparent from the field theory to the gravity dual, making it useful in constructing backgrounds dual to the full Leigh-Strassler family of theories.