Cancelling mod-2 anomalies by Green-Schwarz mechanism with $B_{\mu\nu}$

TL;DR

This paper investigates the conditions under which mod-2 anomalies in gauge theories can be canceled using the Green-Schwarz mechanism involving an antisymmetric tensor field, with specific examples in various dimensions.

Contribution

It provides explicit analysis of mod-2 anomaly cancellation via the Green-Schwarz mechanism in 4d and 8d gauge theories, highlighting cases where it succeeds or fails.

Findings

Mod-2 anomalies in 8d $Sp(n)$ gauge theories can be canceled.

Mod-2 Witten anomalies in 4d $SU(2)$ and $Sp(n)$ gauge theories cannot be canceled.

The results align with known string theory realizations for certain theories.

Abstract

We study if and when mod-2 anomalies can be canceled by the Green-Schwarz mechanism with the introduction of an antisymmetric tensor field $B_{\mu\nu}$. As explicit examples, we examine $SU(2)$ and more general $Sp(n)$ gauge theories in four and eight dimensions. We find that the mod-2 anomalies of 8d $\mathcal{N}=1$ $Sp(n)$ gauge theory can be canceled, as expected from it having a string theory realization, while the mod-2 Witten anomaly of 4d $SU(2)$ and $Sp(n)$ gauge theory cannot be canceled in this manner.