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

TL;DR

The paper analyzes the (2,0) theory of tensor multiplets and self-dual strings in six dimensions, showing that consistency requires cancellation of both classical and quantum anomalies that are proportional to the Euler class of the normal bundle. Using the descent formalism and Dirac quantization, the authors derive an ADE-classification of allowed models, with magnetic charges forming the root lattice of a simply laced Lie algebra and the tensor multiplet values living in the corresponding weight space. In the decoupling limit around a straight string, the world-sheet theory becomes a supersymmetric level-one Wess-Zumino-Witten model on the group (R x SU(2))/Z2, realized through a gauged WZ term and a set of local kinetic terms for the radial, angular, and fermionic fields. These results connect the six-dimensional (2,0) theories to ADE root systems, clarify the structure of anomalies on self-dual strings, and illuminate the 2D world-sheet dynamics that emerge from the higher-dimensional theory.

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 .