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Title: | THE PHYSICAL MATHEMATICS OF VARIOUS QUANTUM FIELD THEORIES | Authors: | PNG KEE SENG | Keywords: | Physics, mathematics, topological, quantum, field, theory | Issue Date: | 12-Aug-2020 | Citation: | PNG KEE SENG (2020-08-12). THE PHYSICAL MATHEMATICS OF VARIOUS QUANTUM FIELD THEORIES. ScholarBank@NUS Repository. | Abstract: | We explain how topologically-twisted N=2 gauge theory on an open four-manifold, will allow physical proofs of various mathematical conjectures and theorems. When the boundary is a Seifert manifold, one can also relate its instanton Floer-homology to an affine-algebra via a two-dimensional A-model with target based loop group. We further demonstrate an action of the affine-algebra on the quantum-cohomology of the moduli space of flat connections on a Riemann-surface, and derive the Verlinde-formula. We also show that four-dimensional Chern-Simons theory is, with Nahm-pole-type boundary-conditions, dual to three-dimensional Toda theory with a novel three-dimensional W-algebra. Embedding four-dimensional Chern-Simons theory in a partial-twist of the five-dimensional maximally-supersymmetric-Yang-Mills theory on a manifold with corners reveals that three-dimensional Toda theory is dual to two-dimensional A-model on Bogomolny moduli space. This novel 3d-2d correspondence also reveals that representations of 3d W-algebra are acted on by the quantized-algebra of certain holomorphic functions on the Bogomolny moduli space. | URI: | https://scholarbank.nus.edu.sg/handle/10635/185721 |
Appears in Collections: | Ph.D Theses (Open) |
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