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.
- Pub Date:
- February 2010
- High Energy Physics - Theory;
- Mathematics - Algebraic Topology;
- Mathematics - Differential Geometry
- 8 pages. v2: Major revision. To appear in the proceedings of String-Math 2011 conference