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The elliptic genus - a view from conformal field theory

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Metric and Analytic Aspects of Moduli Spaces

The elliptic genus of a compact Calabi-Yau manifold Y is a weak Jacobi form of weight zero. It is a topological invariant of Y which allows a reinterpretation as part of the partition function of so-called associated conformal field theories. As such, the coefficients of the elliptic genus count generic dimensions of spaces of states across the moduli space of such theories. On the other hand, if the theories have extended supersymmetry, then this conformal field theoretic view on the elliptic genus implies a novel decomposition of the underlying virtual bundle. This phenomenon occurs, for example, if Y is a hyperKaehler manifold.

The talk will review the elliptic genus from this perspective in terms of geometric data.

This talk is part of the Isaac Newton Institute Seminar Series series.

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