A Classification of Rational Conformal Field Theories with Three Characters and vanishing Wronskian Index.

Chethan Gowdigere

Wed, May. 24th 2023, 14:15-16:15

Salle Claude Itzykson, Bât. 774, Orme des Merisiers

In this talk, a classification scheme for rational conformal field theories (RCFTs), based on the modular linear differential equations (MLDEs) that their characters satisfy, will be explained. In this classification scheme, introduced by Mathur-Mukhi-Sen in 1989, a RCFT is labelled by two integers [n, l] : (i) n is the number of characters and is positive, (ii) l is the Wronskian index and is non-negative. Remarkably, the MLDE that the characters of.RCFT satisfies, is also labelled by the same pair of integers [n, l]. All RCFTs with a given {n, l] solve the MLDE with that [n,l].
The classification of [2,0] RCFTs was achieved in 1989 by Mathur-Mukhi-Sen; this is a list of eight CFTs (the Deligne-series or the MMS-series). The classification problem of [3, 0] RCFTs was set up in 1989 but remained unsolved till the end of 2022. This talk will report on this progress. First, the character-like solutions to the [3, 0] MLDE will be obtained: there are two infinite series and an additional 303. Then, the analysis that identifies [3,0] RCFTs from the character-like solutions to the [3,0] MLDE will be explained. The final complete list of [3, 0] RCFTs includes two infinite affine series B_{r,1}, D_{r,1} and 45 additional theories.

Contact : Ioannis
TSIARES