On 2d Conformal Field Theories with Two Characters

Abstract

Rational CFT's are classified by an integer $\ell$, the number of zeroes of the Wronskian of their characters in moduli space. For $\ell =0$ they satisfy non-singular modular-invariant differential equations, while for $\ell >0$ the corresponding equations have singularities. We survey CFT's with two characters and $\ell =0,2,3,4$ and verify the consistency, at the level of characters, of some candidate theories with $\ell \ne 0$. For $\ell =2$ there are seven consistents sets of characters. We identify specific combinations of level-1 current algebras that are potential symmetries of the corresponding CFT's.

29 pages, expanded with discussion on chiral algebras, final version to appear in JHEP