Séminaire de Physique Mathématique

Cut-and-join Operators in Cohomological Field Theory and Topological Recursion

by Alexander Alexandrov (Center for Geometry and Physics, Pohang, Korea)

Amphithéâtre Léon Motchane (I.H.E.S.)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

We construct a cubic cut-and-join operator description for the partition functions of all semi-simple cohomological field theories, and, more generally, for the partition functions of the Chekhov-Eynard-Orantin topological recursion on a possibly irregular local spectral curve. The cut-and-join description leads to an algebraic version of topological recursion.
For the same partition functions, we also derive N families of the Virasoro constraints and prove that these constraints, supplemented by a deformed dimension constraint, imply the cut-and-join description.

The talk is based on arXiv:2202.09090.

Organized by

Maxim Kontsevich