Topic: 2d CFTs on Magic Triangle

Speaker: Prof. Kimyeong Lee

Coordinates: PCFT C1124, 16:00, Thursday, December 25

Abstract: The Magic Triangle of Cvitanović–Deligne–Gross extends the well-known Freudenthal–Tits–Vinberg Magic Square, which organizes some Lie algebras as symmetry algebras of projective planes over the normed division algebras: the real number, complex number, quaternion, and octonion. In this work, we complete and analyze the full Magic Triangle, in which 30 generalized Lie algebras emerge. Corresponding to each of these algebras, we construct a rational conformal field theory (RCFT), forming a complete set of 30 RCFTs associated with the triangle. Remarkably, we show that at level one, all these theories satisfy a single modular linear differential equation and exhibit a unifying structure via magic coset relations. Furthermore, we demonstrate that these 30 theories can be decomposed into combinations of just five fundamental “atomic” RCFTs. We also explore extensions to higher-level theories within the Magic Triangle and uncover some of  intriguing structural properties. The talk will conclude with a discussion of open questions and future directions.