Elliptic Genera and 3d Gravity

TL;DR

This paper establishes constraints on the elliptic genus of 2d supersymmetric conformal field theories with gravity duals, providing examples and discussing criteria for weakly curved gravity descriptions at large central charge.

Contribution

It derives bounds on the elliptic genus for theories with gravity duals and analyzes which theories satisfy these bounds, advancing understanding of holographic duality in 2d CFTs.

Findings

Certain theories satisfy the elliptic genus bounds

Examples include symmetric product orbifolds of K3 and Monster CFT

Quantifies the fraction of theories with weakly curved gravity duals

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.