Quantum Crystals and Topological Strings

by Domenico Orlando (Institut de Physique-Universite de Neuchatel)

Tuesday 9 Dec 2008, 14:00 → 15:00 Europe/Zurich

TH Theory Conference Room (CERN)

Random partitions appear in many branches of mathematics and physics, such as Gromov-Witten theory, random matrix theory, Seiberg-Witten theory and others. In particular, the partition function of the melting crystal corner, given by the MacMahon function, has been shown to equal the partition function of the topological string A-model with target space C^3. In this talk I will discuss the equivalent crystal melting problem in two and three dimensions. Particular emphasis will be given to the quantized version that is deeply related to the XXZ spin chain. After having shown exact and numerical results I will discuss the properties of these systems as well their relation to stochastic quantization, and implications for topological string theory. Partly based on 0803.1927[cond-mat.stat-mech].