SIMIS+Shanghaitech Joint Seminar on Theoretical Physics: Completeness Relation and Casimir Operator for the Virasoro Algebra

报告人： Jean-Francois Fortin (Laval University)

摘要： We discuss two basic objects of 2d local conformal field theories: the completeness relation and the Casimir operator. First, we propose an explicit expression for the inverse Shapovalov form in terms of the singular vectors and their conformal dimensions, that directly implies a novel expression for the completeness relation. We show that this result can be leveraged in the computation of Virasoro conformal blocks. Second, we determine generic Casimir operators for arbitrary algebras by deriving a recurrence relation in terms of their inverse Shapovalov form and solving it through repeated substitution. For the Virasoro algebra, our answer leads to a partial inversion of the Virasoro/Heisenberg dictionary and might be of interest for integrable models.

时间： 14:00-15:00, Thursday, Dec. 5th, 2024

地点： Auditorium (18th floor), SIMIS
Zoom会议号： 423 317 8953 (Passcode SIMIS)