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KTH/Nordita/SU seminar in Theoretical Physics

Crystals, instantons and quantum geometry

by Richard J. Szabo (Heriot-Watt University, Edinburgh)

122:026 ()


We describe the statistical mechanics of a melting crystal in three dimensions, and its relationships with diverse topics in mathematical physics. On the mathematics side, the model is connected to the combinatorics of plane partitions and the enumeration of Donaldson-Thomas invariants in algebraic geometry. On the physics side, it is related to certain integrable hierarchies, matrix models, Chern-Simons gauge theory, and a toy model of quantum gravity in six dimensions. Its partition function can also be computed by enumerating the contributions from noncommutative instantons to a six-dimensional topological gauge theory; this yields an interpretation of the melting crystal model as a discretization of six-dimensional spacetime at the Planck scale. We also describe analogous relations between a melting crystal model in two dimensions and N=4 supersymmetric Yang-Mills theory in four dimensions.