Comments on Determinant Formulas for General CFTs

Abstract

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.

14 pages, v2: notations and section 2.3 improved, typos corrected, v3: published version

References in corpus (3)

• Bootstrapping Mixed Correlators in the 3D Ising Model
• Comments on Unparticles
• Determinant Formula for Parabolic Verma Modules of Lie Superalgebras

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