Hector Dlamini | Searcharxiv

arXiv2019

Marginal deformations and quasi-Hopf algebras

We establish the existence of a quasi-Hopf algebraic structure underlying the Leigh-Strassler N=1 superconformal marginal deformations of the N=4 Super-Yang-Mills theory. The scalar-sector R-matrix of these theories, which is related to their one-loop spin chain Hamiltonian, does not generically satisfy the Quantum Yang-Baxter Equation. By constructing a Drinfeld twist which relates this R-matrix to that of the N=4 SYM theory, but also produces a non-trivial co-associator, we show that the generic Leigh-Strassler R-matrix satisfies the quasi-Hopf version of the QYBE. We also use the twist to define a suitable star product which directly relates the N=4 SYM superpotential to that of the marginally deformed gauge theories. We expect our results to be relevant to studies of integrability (and its breaking) in these theories, as well as to provide useful input for supergravity solution-generating techniques.

hep-th↗

arXiv2016

Integrable Hopf twists, marginal deformations and generalised geometry

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.

hep-th↗