Two-dimensional sigma-models with a first-order Lagrangian are particularly interesting both from a physical and a mathematical point of view. Physically they can arise from ordinary sigma-models in a topological limit, but they can also be of independent interest as in Berkovits’ pure spinor string. Mathematically they allow to generalize the notion of vertex operator algebra. I will discuss the problem of computing the partition function, or elliptic genus, for such systems and some proposals for the solution.

LPT-ENS