Noncommutative GUT inspired theories and the UV finiteness of the fermionic four point functions

TL;DR

This paper demonstrates that in noncommutative GUT inspired theories, fermionic four-point functions are UV finite at one-loop, contrasting with general noncommutative gauge theories, supporting their viability over non-GUT models.

Contribution

It shows UV finiteness of fermionic four-point functions in noncommutative GUT inspired theories at one-loop, highlighting their potential advantages over other noncommutative gauge theories.

Findings

Fermionic four-point functions are UV finite at one-loop in noncommutative GUT theories.

This finiteness contrasts with the non-GUT noncommutative gauge theories.

Results favor noncommutative GUTs and GUT-inspired models over other noncommutative gauge theories.

Abstract

We show at one-loop and first order in the noncommutativity parameters that in any noncommutative GUT inspired theory the total contribution to the fermionic four point functions coming only from the interaction between fermions and gauge bosons, though not UV finite by power counting, is UV finite at the end of the day. We also show that this is at odds with the general case for noncommutative gauge theories --chiral or otherwise-- defined by means of Seiberg-Witten maps that are the same --barring the gauge group representation-- for left-handed spinors as for right-handed spinors. We believe that the results presented in this paper tilt the scales to the side of noncommutative GUTS and noncommutative GUT inspired versions of the Standard Model.