Noncommutative fermions and Morita equivalence

TL;DR

This paper investigates Morita equivalence in noncommutative fermion theories on two-tori, demonstrating an equivalence between abelian and nonabelian theories for rational theta and confirming this at the level of anomalies and determinants.

Contribution

It establishes Morita equivalence for fermion theories on noncommutative two-tori, including anomaly and Dirac operator determinant analysis, for rational theta values.

Findings

Equivalence between abelian and nonabelian fermion theories for rational theta.

Morita equivalence holds at the level of chiral anomaly.

Determinant of the Dirac operator is preserved under the duality.

Abstract

We study the Morita equivalence for fermion theories on noncommutative two-tori. For rational values of the $\theta$ parameter (in appropriate units) we show the equivalence between an abelian noncommutative fermion theory and a nonabelian theory of twisted fermions on ordinary space. We study the chiral anomaly and compute the determinant of the Dirac operator in the dual theories showing that the Morita equivalence also holds at this level.