Induced Chern-Simons action on noncommutative torus

TL;DR

This paper calculates a Chern-Simons term induced by fermions on a noncommutative torus, revealing a new mixed term for rational noncommutativity that involves periodic gauge fields similar to crystal structures.

Contribution

It introduces a novel mixed Chern-Simons term on noncommutative tori for rational , linking noncommutative geometry with periodic gauge field interactions.

Findings

Discovery of a new mixed Chern-Simons term for rational 

Identification of -periodic gauge field interactions

Revealing connections between noncommutative geometry and crystal-like structures

Abstract

We compute a Chern-Simons term induced by the fermions on noncommutative torus interacting with two U(1) gauge fields. For rational noncommutativity \theta \propto P/Q we find a new mixed term in the action which involves only those fields which are (2\pi)/Q periodic, like the fields in a crystal with Q^2 nodes.