Renormalisability of noncommutative GUT inspired field theories with anomaly safe groups

Understand

We consider noncommutative GUT inspired field theories formulated within the enveloping-algebra formalism for anomaly safe compact simple gauge groups.

• Our theories have only gauge fields and fermions, and we compute the UV divergent part of the one-loop background-field effective action involving two fermionic fields at first order in the noncommutativity parameter theta.
• We show that, if the second-degree Casimir has the same value for all the irreps furnished by the fermionic multiplets of the model, then, that UV divergent part can be renormalised by carrying out multiplicative renormalisations of the coupling constant, theta and the fields, along with the inclusion of theta-dependent counterterms which vanish upon imposing the equations of motion.
• These theta-dependent counterterms have no physical effect since they vanish on-shell.