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Self-Dual Strings in Six Dimensions: Anomalies, the ADE-Classification, and the World-Sheet WZW-Model

2005; Springer Science+Business Media; Volume: 257; Issue: 2 Linguagem: Inglês

10.1007/s00220-005-1324-7

1432-0916

Måns Henningson,

Noncommutative and Quantum Gravity Theories

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 .