Abstract
Given a two-dimensional quantum field theory with (0,2) supersymmetry, one can construct a chiral (or vertex) algebra. The chiral algebra of a (0,2) supersymmetric sigma model is, perturbatively, the cohomology of a sheaf of chiral differential operators on a string Kähler manifold. However, it vanishes in some cases when instantons are taken into account. I will discuss the implication of this phenomenon for the Höhn-Stolz conjecture on the Witten genus.
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