On classification of fermionic rational conformal field theories

A bstract We systematically study how the integrality of conformal characters shapes space fermionic rational field theories in two dimensions. The suggests that on torus with a given choice spin structures should be invariant under principal congruence subgroup PSL(2 , ℤ). invariance strongly constrains possible values central charge as well weights both Neveu-Schwarz and Ramond sectors, which improves conventional holomorphic modular bootstrap method significant manner. This allows us to make much progress classification number independent less than five.