Anomaly matching and a Hopf-Wess-Zumino term in six-dimensional, N = (2,0) field theories

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 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. (C) 2000 Elsevier Science B.V. All rights reserved.