We derive an exact expression for the Fourier coefficients of elliptic genera of Calabi-Yau manifolds. When applied to k-fold symmetric products of K3 surfaces the expression is well-suited to studying the AdS/CFT correspondence on AdS3 x S3. The expression also elucidates an SL(2,Z) invariant phase diagram for the D1/D5 system involving deconfining transitions in the limit as k goes to infinity.
Cite
@article{arxiv.hep-th/0005003,
title = {A Black Hole Farey Tail},
author = {Robbert Dijkgraaf and Juan Maldacena and Gregory Moore and Erik Verlinde},
journal= {arXiv preprint arXiv:hep-th/0005003},
year = {2007}
}
Comments
54 pages, harvmac b-mode. 9 figures; minor mistakes corrected; V3: An important mistake has been corrected. Conclusions essentially unchanged