Non-chiral 2d CFT with integer energy levels

Understand

The partition function of 2d conformal field theory is a modular invariant function.

• It is known that the partition function of a holomorphic CFT whose central charge is a multiple of 24 is a polynomial in the Klein function.
• In this paper, by using the medium temperature expansion we show that every modular invariant partition function can be mapped to a holomorphic partition function whose structure can be determined similarly.
• We use this map to study partition function of CFTs with half-integer left and right conformal weights.