The Geometric Construction of WZW Effective Action in Non-commutative Manifold

TL;DR

This paper develops a geometric method to construct the WZW effective action on high-dimensional non-commutative manifolds, showing that the resulting anomalies match known results in four-dimensional cases.

Contribution

It introduces a novel geometric construction of the WZW effective action in non-commutative spaces, extending previous approaches to higher dimensions.

Findings

Constructed WZW effective Lagrangian in non-commutative spaces

Derived consistent anomalies in four-dimensional non-commutative space

Confirmed anomalies coincide with established results by Bonora et al.

Abstract

By constructing close one cochain density ${\Omega^1}_{2n}$ in the gauge group space we get WZW effective Lagrangian on high dimensional non-commutative space.Especially consistent anomalies derived from this WZW effective action in non-commutative four-dimensional space coincides with those by L.Bonora etc.