Abelian Varieties, RCFTs, Attractors, and Hitchin Functional in Two Dimensions
Abstract
We consider a generating function for the number of conformal blocks in rational conformal field theories with an even central charge c on a genus g Riemann surface. It defines an entropy functional on the moduli space of conformal field theories and is captured by the gauged WZW model whose target space is an abelian variety. We study a special coupling of this theory to twodimensional gravity. When c=2g, the coupling is nontrivial due to the gravitational instantons, and the action of the theory can be interpreted as a twodimensional analog of the Hitchin functional for CalabiYau manifolds. This gives rise to the effective action on the moduli space of Riemann surfaces, whose critical points are attractive and correspond to Jacobian varieties admitting complex multiplication. The theory that we describe can be viewed as a dimensional reduction of topological Mtheory.
 Publication:

arXiv eprints
 Pub Date:
 April 2006
 arXiv:
 arXiv:hepth/0604176
 Bibcode:
 2006hep.th....4176S
 Keywords:

 High Energy Physics  Theory
 EPrint:
 54 pages, harvmac