Maxim Kontsevich - IHES
Wednesday, June 8, 10:45AM (Zoom meeting starts at 10:30)
“Over-determined Schwinger-Dyson equations for matrix models”
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.