Communications in Number Theory and Physics

Volume 2 (2008)

Number 4

Extremal $\CN=(2,2)$ 2D conformal field theories and constraints of modularity

Pages: 743 – 801



Matthias R. Gaberdiel (Institut für Theoretische Physik, ETH Zurich, Switzerland)

Sergei Gukov (Department of Physics and Department of Mathematics, University of California at Santa Barbara)

Christoph A. Keller (Institut für Theoretische Physik, ETH Zurich, Switzerland)

Gregory W. Moore (NHETC and Department of Physics and Astronomy, Rutgers University, New Jersey)

Hirosi Ooguri (California Institute of Technology, Pasadena)


We explore the constraints on the spectrum of primaryfields\break implied by modularity of the elliptic genusof $\CN=(2,2)$ 2D CFTs. We show that such constraints havenontrivial implications for the existence of “extremal”$\CN=(2,2)$ conformal field theories. Applications toAdS$_3$ supergravity and flux compactifications areaddressed.

Published 1 January 2008