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In this talk I will discuss an interesting phenomenon, namely a correspondence between sigma models and vertex operator algebras, with the two related by their symmetry properties and by a reflection
procedure, mapping the right-movers of the sigma model at a special
point in the moduli space to left-movers. We will discuss the examples
of N=(4,4) sigma models on $T^4$ and on $K3$. The talk will be based
on joint work with Vassilis Anagiannis, John Duncan and Roberto