Refined geometric transition and local P2
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Date
2022
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Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022.
Abstract
In this thesis, the approaches for calculating refined topological string amplitudes on compact Calabi-Yaus for the case local P^2 are investigated. One approach is making use of large N duality and refined Chern-Simons theory (Aganagic and Shakirov) and the other is defining another vertex (Iqbal, Kozçaz). It turns out that this new vertex can be obtained from refined Chern-Simons theory using properties of Macdonald and Schur functions, in this thesis we outline the way of this derivation. Aside from a brief review of topological strings, large N duality and knot invariants that can be calculated using Chern-Simons theory, a review of topological vertex formalism and its derivation using Chern-Simons theory, both in the refined and unrefined case is included.