Anomaly Matching and a Hopf-Wess-Zumino Term in 6d, N=(2,0) Field Theories

TL;DR

This paper reveals a new Wess-Zumino term in 6d N=(2,0) theories related to the Hopf invariant, fixed by anomaly matching, with implications for M5 branes and skyrmionic strings.

Contribution

It introduces a novel Hopf-Wess-Zumino term in 6d N=(2,0) theories and relates it to anomaly matching and brane configurations.

Findings

The Wess-Zumino term is linked to the Hopf invariant of rac7(S^4)

The coefficient of the Wess-Zumino term is proportional to N(N+1) for N M5 branes

Skyrmionic strings are proposed to be W-boson strings.

Abstract

We point out that the low energy theory of 6d, N=(2,0) field theories, when away from the origin of the moduli space of vacua, necessarily includes a new kind of Wess-Zumino term. The form of this term is related to the Hopf invariant associated with \pi_7 (S^4). The coefficient of the Wess-Zumino term is fixed by an anomaly matching relation for a global flavor symmetry. For example, in the context of a single M5 brane probe in the background of N distant M5 branes, the probe must have the Hopf-WZ term with coefficient proportional to N(N+1). Various related checks and observations are made. We also point out that there are skyrmionic strings, and propose that they are the W-boson strings.