Higher Structure Conferences Wendland

The elliptic genus revisited

Abstract: For the special case of compact Calabi-Yau manifolds, we recall the definition of the elliptic genus as a regularized index of a Dirac operator on the free loop space. We revisit this definition from the viewpoint of (two-dimensional unitary Euclidean) conformal field theory and superconformal vertex algebras, along with their symmetries.

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