# (15.10.) Bounding the heat trace of a Calabi-Yau manifold

Johannes Walcher (Heidelberg)

15.10.2015 at 16:15

The SCHOK bound states that the number of marginal deformations of certain two-dimensional conformal field theories is bounded linearly from above by the number of relevant operators. We analyze the prospects of finding an independent a priori bound on the number of relevant operators in conformal field theories defined via sigma models into Calabi-Yau manifolds. We argue that a bound on the trace of the scalar heat kernel that is uniform in the topology would be sufficient for this purpose, and show explicitly that the most generic type of curvature singularity is compatible with such a bound.

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