Gravity and nonabelian gauge fields in noncommutative space-time

TL;DR

This paper extends noncommutative geometric gravity models to include nonabelian gauge fields, revealing conditions under which the generalized action remains gauge invariant, aligning with electroweak and strong interaction theories.

Contribution

It demonstrates the incorporation of nonabelian gauge fields into noncommutative gravity frameworks, identifying specific gauge group configurations that preserve invariance.

Findings

Gauge invariance is maintained when one sheet has abelian and the other nonabelian gauge groups.

Theories of electroweak and strong interactions correspond to the two cases of gauge group configurations.

The generalized Hilbert-Einstein action's invariance depends on the gauge group structure across spacetime sheets.

Abstract

Noncommutative geometric construction of gravity in the two sheeted spacetime can be viewed as a discretized version of a Kaluza-Klein theory. In this paper, we show that it is possible to incorporate the nonabelian gauge fields in the same framework. The generalized Hilbert-Einstein action is gauge invariant only in two cases. In the first case, the gauge group must be abelian on one sheet of spacetime and nonabelian on the other one. In the second case, the gauge group must be the same on two sheets of spacetime. Actually, the theories of electroweak and strong interactions are exactly these two cases.