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The elliptic genus - a view from conformal field theory

Presented by: 
KA Wendland Universität Freiburg
Thursday 30th July 2015 - 16:00 to 17:00
INI Seminar Room 1
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.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons