Spinors on a curved noncommutative space: coupling to torsion and the Gross-Neveu model

TL;DR

This paper explores spinor actions on a curved noncommutative space, specifically the truncated Heisenberg algebra, and demonstrates how dimensional reduction leads to a noncommutative Gross-Neveu model that is fully renormalisable.

Contribution

It introduces a nonminimal coupling of spinors to torsion on a curved noncommutative space and connects it to a renormalisable noncommutative Gross-Neveu model.

Findings

Dimensional reduction yields a noncommutative Gross-Neveu model.

The model is shown to be fully renormalisable.

Coupling of spinors to torsion is analyzed in the noncommutative setting.

Abstract

We analyse the spinor action on a curved noncommutative space, the so-called truncated Heisenberg algebra, and in particular, the nonminimal coupling of spinors to the torsion. We find that dimensional reduction of the Dirac action gives the noncommutative extension of the Gross-Neveu model, the model which is, as shown by Vignes-Tourneret, fully renormalisable.