The Minimal and the New Minimal Supersymmetric Grand Unified Theories on Noncommutative Space-time

TL;DR

This paper develops noncommutative versions of minimal and new minimal supersymmetric GUTs using the enveloping-algebra formalism, with a novel Higgs sector formulation based on Clifford algebra elements.

Contribution

It introduces a construction method for noncommutative supersymmetric GUTs and details the Higgs sector formulation using Clifford algebra, advancing noncommutative GUT models.

Findings

Successful formulation of noncommutative minimal and new minimal supersymmetric GUTs

Higgs fields realized as elements of Clifford algebra Cl10(C)

Supersymmetry linearly realized in noncommutative fields

Abstract

We construct noncommutative versions of both the minimal and the new minimal supersymmetric Grand Unified Theories. The enveloping-algebra formalism is used to carry out such constructions. The beautiful formulation of the Higgs sector of these noncommutative theories is a consequence of fact that, in the GUTs at hand, the ordinary Higgs fields can be realized as elements of the Clifford algebra Cl10(C). In the noncommutative supersymmetric GUTs we formulate, supersymmetry is linearly realized by the noncommutative fields; but it is not realized by the ordinary fields that define those noncommutative fields via the Seiberg-Witten map.