Rational Conformal Field Theories and Complex Multiplication
View/ Open
Author
Gukov, Sergei
Vafa, Cumrun
Published Version
https://doi.org/10.1007/s00220-003-1032-0Metadata
Show full item recordCitation
Gukov, Sergei, and Cumrun Vafa. 2004. “Rational Conformal Field Theories and Complex Multiplication.” Communications in Mathematical Physics 246 (1): 181–210. https://doi.org/10.1007/s00220-003-1032-0.Abstract
We study the geometric interpretation of two dimensional rational conformal field theories, corresponding to sigma models on Calabi-Yau manifolds. We perform a detailed study of RCFT's corresponding to the T-2 target and identify the Cardy branes with geometric branes. The T-2's leading to RCFT's admit ''complex multiplication'' which characterizes Cardy branes as specific D0-branes. We propose a condition for the conformal sigma model to be RCFT for arbitrary Calabi-Yau n-folds, which agrees with the known cases. Together with recent conjectures by mathematicians it appears that rational conformal theories are not dense in the space of all conformal theories, and sometimes appear to be finite in number for Calabi-Yau n-folds for n>2. RCFT's on K3 may be dense. We speculate about the meaning of these special points in the moduli spaces of Calabi-Yau n-folds in connection with freezing geometric moduli.Terms of Use
This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAACitable link to this page
http://nrs.harvard.edu/urn-3:HUL.InstRepos:41385007
Collections
- FAS Scholarly Articles [18292]
Contact administrator regarding this item (to report mistakes or request changes)