Annales Henri Poincaré

, Volume 17, Issue 10, pp 2623–2662 | Cite as

Elliptic Genera and 3d Gravity

  • Nathan Benjamin
  • Miranda C. N. ChengEmail author
  • Shamit Kachru
  • Gregory W. Moore
  • Natalie M. Paquette
Open Access


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.


Black Hole Partition Function Modulus Space Modular Form Elliptic Genus 
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© The Author(s) 2016

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Authors and Affiliations

  • Nathan Benjamin
    • 1
    • 2
  • Miranda C. N. Cheng
    • 3
    Email author
  • Shamit Kachru
    • 1
    • 2
  • Gregory W. Moore
    • 4
  • Natalie M. Paquette
    • 1
    • 2
  1. 1.Stanford Institute for Theoretical PhysicsStanford UniversityStanfordUSA
  2. 2.SLAC National Accelerator LaboratoryMenlo ParkUSA
  3. 3.Institute of Physics and Korteweg-de Vries Institute for MathematicsUniversity of AmsterdamAmsterdamThe Netherlands
  4. 4.NHETC and Department of Physics and AstronomyRutgers UniversityPiscatawayUSA

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