Noncommutative Gravity in Six Dimensions

TL;DR

This paper develops a gauge theory of gravity in six-dimensional non-commutative space-time using the U(2,2) gauge group, revealing first-order corrections in the non-commutativity parameter after applying the Seiberg-Witten map.

Contribution

It introduces a novel 6D non-commutative gravity model with the U(2,2) gauge group, showing first-order non-commutative corrections distinct from previous SO-based models.

Findings

First-order corrections in non-commutativity parameter  after Seiberg-Witten map.

Gauge group U(2,2) includes Lorentz group SO(4,2) as a subgroup.

Contrasts with SO(d,1) gauge theories where corrections appear at different orders.

Abstract

A gauge theory of gravity is defined in 6 dimensional non-commutative space-time. The gauge group is the unitary group U(2,2), which contains the homogeneous Lorentz group, SO(4,2), in 6 dimensions as a subgroup. It is shown that, after the Seiberg-Witten map, in the corresponding theory the lowest order corrections are first order in the non-commutativity parameter \theta. This is in contrast with the results found in non-commutative gauge theories of gravity with the gauge group SO(d,1).