Comments on Determinant Formulas for General CFTs

Understand

We point out that the determinant formula for a parabolic Verma module plays a key role in the study of (super)conformal field theories and in particular their (super)conformal blocks.

• The determinant formula is known from the old work of Jantzen for bosonic conformal algebras, and we present a conjecture for superconformal algebras.
• The application of the formula includes derivation of the unitary bound and recursion relations for conformal blocks.