Subscribe to Events

Download as iCal file

Mathematical Physics Seminar

Over-determined Schwinger-Dyson equations for matrix models

Maxim Kontsevich - IHES

Location:  Zoom
Date & time: Wednesday, 08 June 2022 at 10:45AM - 11:45AM

Observables in the planar limit of multi-matrix models satisfy an infinite system of quadratic equations,  called loop equations (analogs of Schwinger-Dyson equations, meaning  that the integral of a total derivative is zero).  Naive counting gives more equations than variables, i.e. the system of loop equations is over-determined. Nevertheless, it has non-trivial solutions, depending on a finite or infinite number of parameters, depending on the model. I'll talk about the cohomological mechanism behind this phenomenon.