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)

Europe/Paris
Amphithéâtre Léon Motchane (I.H.E.S.)

Amphithéâtre Léon Motchane

I.H.E.S.

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

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

Contact