From noncommutative Yang-Mills to noncommutative gravity through a classical double copy map

TL;DR

This paper derives the first noncommutative correction to Einstein-Hilbert gravity from a double copy of noncommutative Yang-Mills theory, revealing new geometric structures and corrections in a doubled field theory framework.

Contribution

It introduces a novel double copy construction for noncommutative theories, including noncommutative corrections to double field theory and gravity.

Findings

Computed noncommutative corrections to three-point vertices in ncYM

Constructed a double copy theory incorporating noncommutative effects

Identified $ heta^2$-corrections to the cubic double field theory action

Abstract

We compute the first nontrivial noncommutative correction to the Einstein-Hilbert Lagrangian, which arises from the double copy of noncommutative Yang-Mills theory (ncYM). We start by considering linear and quadratic $\theta$-corrections up to cubic order in fields in ncYM theory and in arbitrary $D$ dimensions. We compute the first nontrivial corrections to the three-points vertex operators and use them to construct a double copy theory of the form ncYM $\times$ ncYM. The resulting theory is given by a double geometrical formalism which includes noncommutative corrections to the perturbative cubic double field theory (DFT) formulation, where the star product of the theory is doubled in agreement with the doubling of the physical coordinates of the theory. Upon solving the level matching condition the noncommutative products are identified and they produced $\theta^2$-corrections to the cubic DFT action. We analyze the pure gravitational limit of this formulation considering $D=4$ and imposing the transverse-traceless gauge.