Douglas Lundholm: Spectral theory of the Weighted Supermembrane Toy Model

The so-called supersymmetric matrix models have been proposed to describe in a certain sense a unified picture of the fundamental physical interactions. In investigating the spectral features of these models, it has proved useful to consider a highly simplified model in two dimensions, called the supermembrane toy model, or the supersymmetric x²y² potential.

In this talk it will be shown that a modification of this model, involving an extension of its Hilbert space of physical states, opens up a new and promising approach to the investigation of ground states of the matrix models. The key to this approach is a proof that a certain matrix-valued Schrodinger operator has finitely many negative eigenvalues.

The talk will be given at a level suitable for Ph.D. students with no background in spectral theory. (If there is interest, the speaker would be happy to give a more detailed seminar in the future.)