Calabi-Yau crystals in topological string theory

Details Calabi-Yau crystals in topological string theory Calabi-Yau crystals in topological string theory

2007-12-13

arxiv.org/abs/0712.2173v1

Physics

High Energy Physics

High Energy Physics - Theory

PhD thesis, June 2007, 200 pages, introductory chapter in Polish

Scientific paper

This thesis is concerned with a realisation of topological theories in terms of statistical models known as Calabi-Yau crystals. The thesis starts with an introduction and review of topological field and string theories. Subsequently several new results are presented. The main focus of the thesis is on the topological string theory. In this case crystal models correspond to three-dimensional partitions and their relations with the topological vertex theory and knot invariants are studied. Two-dimensional crystal models corresponding to topological gauge theories on ALE spaces are also introduced and analysed. Essential mathematical tools are summarised in appendices.

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