Integrable Hopf twists, marginal deformations and generalised geometry

TL;DR

This paper explores how quantum group symmetries from marginal deformations of N=4 SYM can be represented in gravity duals using generalised geometry, leading to new supergravity solutions.

Contribution

It demonstrates how Hopf algebra twists associated with Leigh-Strassler deformations can be incorporated into gravity duals via generalised geometry, extending the Lunin-Maldacena solutions.

Findings

Constructed star product encoding deformed symmetry

Deformed pure spinors lead to new supergravity solutions

Reproduced known duals using Hopf algebra and generalised geometry

Abstract

The Leigh-Strassler family of N=1 marginal deformations of the N=4 SYM theory admits a Hopf algebra symmetry which is a quantum group deformation of the SU(3) part of the R-symmetry of the Ncal=4 theory. We investigate how this quantum symmetry might be expressed on the gravity side of the AdS/CFT correspondence. First, we discuss the twist leading to the Hopf algebra structure for the well-known beta-deformation as well as a unitarily equivalent theory that we call the w-deformation. We then show how this Hopf twist can be used to define a star product between the three scalar superfields of these theories which encodes the deformed global symmetry. Turning to the gravity side, we adapt this star product to deform the pure spinors of six-dimensional flat space in its generalised geometry description. This leads to an N=2 NS-NS solution of IIB supergravity. Starting from this precursor solution, adding D3-branes and taking the near-horizon limit reproduces the dual gravitational solution to the above theories, first derived by Lunin and Maldacena using TsT techniques. This indicates that the Hopf algebra symmetry can play a useful role in constructing the supergravity duals of the general Leigh-Strassler deformations.