Abstract. Trace map on deformation quantized algebra leads to the algebraic index theorem. We investigate a two-dimensional chiral analogue of the algebraic index theorem via the theory of chiral algebras developed by Beilinson and Drinfeld. We construct a trace map on the elliptic chiral homology of the free beta gamma-bc system using the BV quantization framework. As an example, we compute the trace evaluated on the unit constant chiral chain and obtain the formal Witten genus in the Lie algebra cohomology. This talk is based on joint work with Si Li.
This will be a hybrid seminar. All are very welcome to join either online or in person. Venue: Luigi Stasi Seminar Room (ICTP Leonardo Da Vinci Building), for those wishing to attend in person.