Abstract
We describe general constraints on the elliptic genus of a 2d supersymmetric
conformal field theory which has a gravity dual with large radius in Planck
units. We give examples of theories which do and do not satisfy the bounds we
derive, by describing the elliptic genera of symmetric product orbifolds of
\$K3\$, product manifolds, certain simple families of Calabi-Yau hypersurfaces,
and symmetric products of the "Monster CFT." We discuss the distinction between
theories with supergravity duals and those whose duals have strings at the
scale set by the AdS curvature. Under natural assumptions we attempt to
quantify the fraction of (2,2) supersymmetric conformal theories which admit a
weakly curved gravity description, at large central charge.
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