High Energy Theory Seminar
Supersymmetric gauge theories in various spacetime dimensions lead to enumerative problems: counting of holomorphic curves in Calabi-Yau manifolds, intersection theory on moduli spaces of instantons, limit shapes for random Young diagrams in two and three dimensions. The latter problem is related to dimer models and the models of crystal melting. We shall report on the recent developments in four dimensions, the ultimate dimension for crystal melting coming from supersymmetric gauge theory. The string theory context of the problem is the counting of bound states of D0 branes in the presence of the D8-antiD8 branes and a B-field. The random configurations are tilings of the 3-space by four types of squashed cubes. The similar problem of D0-D6 brane counting led to the partition function which was conjectured in 2004 to be given by the (square of the) Witten index of 11d supergravity. The conjecture was proven in 2015 by A.Okounkov. I will present the conjecture on the partition function of the new model. The M-theory interpretation of the problem remains a mystery.