Anomalies and Supersymmetry

TL;DR

This paper explores quantum field theory anomalies, focusing on their relation to diffeomorphisms and supersymmetry, and discusses methods to systematically solve the associated consistency conditions using anomaly inflow and descent techniques.

Contribution

It introduces systematic methods for solving supersymmetry anomaly consistency conditions and extends the BRST algebra to include diffeomorphism anomalies in a supersymmetric context.

Findings

Supersymmetric Chern-Simons actions can supersymmetrize flavor anomalies.

The BRST algebra extension allows for consistent treatment of diffeomorphism anomalies.

The methods apply to various dimensions and supersymmetry configurations.

Abstract

We revisit quantum field theory anomalies, emphasizing the interplay with diffeomorphisms and supersymmetry. The Ward identities of the latter induce Noether currents of all continuous symmetries, and we point out how these consistent currents are replaced by their covariant form through the appearance of the Bardeen-Zumino currents, which play a central role in our study. For supersymmetry Ward identities, two systematic methods for solving the Wess-Zumino consistency conditions are discussed: anomaly inflow and anomaly descent. The simplest inflows are from supersymmetric Chern-Simons actions in one dimension higher, which are used to supersymmetrize flavor anomalies in $d=4$ and, for $d=2$ $\mathcal{N}=(p,q)$, flavor anomalies with $p,q\leq 3$ and Lorentz-Weyl anomalies with $p,q\leq 6$. Finally, we extend the BRST algebra and the subsequent descent, a necessity for the diffeomorphism anomaly in retrospect. The same modification computes the supersymmetrized anomalies, and determines the above Chern-Simons actions when these exist.