Comments on Chern-Simons Contact Terms in Three Dimensions

TL;DR

This paper investigates the physical significance of contact terms related to Chern-Simons actions in 3D quantum field theories, highlighting their role in anomalies and duality tests, with exact computations via localization.

Contribution

It clarifies the physical meaning of fractional contact terms and demonstrates their computation in supersymmetric theories, providing new insights into anomalies and dualities.

Findings

Fractional contact terms are physical observables.

Localization allows exact computation of these contact terms.

Some contact terms indicate anomalies in supersymmetric theories.

Abstract

We study contact terms of conserved currents and the energy-momentum tensor in three-dimensional quantum field theory. They are associated with Chern-Simons terms for background fields. While the integer parts of these contact terms are ambiguous, their fractional parts are meaningful physical observables. In N=2 supersymmetric theories with a U(1)_R symmetry some of these observables lead to an anomaly. Moreover, they can be computed exactly using localization, leading to new tests of dualities.