An algebraic approach to minimal models in CFTs

Abstract

CFTs are naturally defined on Riemann surfaces. The rational ones can be solved using methods from algebraic geometry. One particular feature is the covariance of the partition function under the mapping class group. In genus $g=1$, this yields modular forms, which can be linked to ordinary differential equations of hypergeometric type with algebraic solutions.Comment: 30 pages. Revised and extended version. (The paper was originally part of arXiv:1305.0469, which had been split into the present paper and arXiv:1705.07627.