  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 .
