Heat kernel, effective action and anomalies in noncommutative theories

TL;DR

This paper computes heat kernel coefficients for generalized Laplacians on the Moyal plane, analyzing effective actions, vacuum energy, and axial anomalies in noncommutative field theories with both local and nonlocal terms.

Contribution

It introduces new calculations of heat kernel coefficients for Laplacians with left and right multiplications on the Moyal plane, including star-nonlocal terms, and explores their implications for anomalies and effective actions.

Findings

Derived heat kernel coefficients with star-local and star-nonlocal terms.

Analyzed large mass and noncommutativity limits of effective action.

Studied axial anomalies in noncommutative gauge theories.

Abstract

Being motivated by physical applications (as the phi^4 model) we calculate the heat kernel coefficients for generalised Laplacians on the Moyal plane containing both left and right multiplications. We found both star-local and star-nonlocal terms. By using these results we calculate the large mass and strong noncommutativity expansion of the effective action and of the vacuum energy. We also study the axial anomaly in the models with gauge fields acting on fermions from the left and from the right.