Quadratic twist-noncommutative gauge theory

TL;DR

This paper constructs a Yang-Mills action on a quadratically-noncommutative spacetime using a Drinfeld twist, extending noncommutative gauge theories beyond constant noncommutativity and proposing a new AdS/CFT dual candidate.

Contribution

It introduces a novel Yang-Mills action on quadratically-noncommutative spacetime derived from a Drinfeld twist, expanding the scope of noncommutative gauge theories.

Findings

Constructed a Yang-Mills action with star-gauge symmetry on quadratically-noncommutative spacetime.

Applied the framework to supersymmetric Yang-Mills theory, proposing a new AdS/CFT dual.

Suggests the deformed theory is expected to be integrable in the planar limit.

Abstract

Studies of noncommutative gauge theory have mainly focused on noncommutative spacetimes with constant noncommutative structure, with little known about actions for noncommutative 4D Yang-Mills theory beyond this case. We construct an action for Yang-Mills theory on a quadratically-noncommutative spacetime, i.e. of quantum-plane type, obtained from a Drinfeld twist, with star-gauge symmetry. Applied to supersymmetric Yang-Mills theory, this gives a candidate AdS/CFT dual of string theory on a related deformation of AdS$_5\times$S$^5$, which is expected to be integrable in the planar limit.