Yukawa terms in noncommutative SO(10) and E6 GUTs

TL;DR

This paper develops a method to construct Yukawa interactions in noncommutative SO(10) and E6 GUTs using the enveloping-algebra formalism, ensuring BRS invariance and renormalizability at first order in the noncommutativity parameter.

Contribution

It introduces a general approach for formulating Yukawa terms in noncommutative GUTs within the enveloping-algebra framework, emphasizing BRS invariance and renormalizability.

Findings

Constructed the most general noncommutative Yukawa terms at first order in theta.

Ensured BRS invariance of the Yukawa interactions.

Demonstrated renormalizability at first order in the noncommutativity parameter.

Abstract

We propose a method for constructing Yukawa terms for noncommutative SO(10) and E6 GUTs, when these GUTs are formulated within the enveloping-algebra formalism. The most general noncommutative Yukawa term that we propose contains, at first order in thetamunu, the most general BRS invariant Yukawa contribution whose only dimensionful parameter is the noncommutativity parameter. This noncommutative Yukawa interaction is thus renormalisable at first order in thetamunu.