Self-dual strings in six dimensions: Anomalies, the ADE-classification, and the world-sheet WZW-model

TL;DR

This paper studies anomalies in six-dimensional (2,0) supersymmetric theories with self-dual strings, revealing an ADE-classification constraint and deriving a supersymmetric WZW model for low-energy string fluctuations.

Contribution

It identifies anomaly cancellation conditions leading to an ADE-classification and constructs the low-energy world-sheet theory as a supersymmetric WZW model.

Findings

Anomalies are proportional to the Euler class of the normal bundle.

Anomaly cancellation imposes ADE-classification constraints.

Low-energy fluctuations are described by a supersymmetric WZW model.

Abstract

We consider the (2, 0) supersymmetric theory of tensor multiplets and self-dual strings in six space-time dimensions. Space-time diffeomorphisms that leave the string world-sheet invariant appear as gauge transformations on the normal bundle of the world-sheet. The naive invariance of the model under such transformations is however explicitly broken by anomalies: The electromagnetic coupling of the string to the two-form gauge field of the tensor multiplet suffers from a classical anomaly, and there is also a one-loop quantum anomaly from the chiral fermions on the string world-sheet. Both of these contributions are proportional to the Euler class of the normal bundle of the string world-sheet, and consistency of the model requires that they cancel. This imposes strong constraints on possible models, which are found to obey an ADE-classification. We then consider the decoupled world-sheet theory that describes low-energy fluctuations (compared to the scale set by the string tension) around a configuration with a static, straight string. The anomaly structure determines this to be a supersymmetric version of the level one Wess-Zumino-Witten model based on the group (R x SU(2))/Z_2 .