Skip navigation
Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01zw12z768m
 Title: Aspects Of Supergroup Chern-Simons Theories Authors: Mikhaylov, Victor Advisors: Witten, Edward Contributors: Physics Department Keywords: Chern-Simons TheoryKnot InvariantsLie SupergroupsTopological Quantum Field Theory Subjects: Physics Issue Date: 2015 Publisher: Princeton, NJ : Princeton University Abstract: The three-dimensional Chern-Simons gauge theory is a topological quantum field theory, whose correlation functions give metric-independent invariants of knots and three-manifolds. In this thesis, we consider a version of this theory, in which the gauge group is taken to be a Lie supergroup. We show that the analytically-continued version of the supergroup Chern-Simons theory can be obtained by topological twisting from the low energy effective theory of the intersection of D3- and NS5-branes in the type IIB string theory. By S-duality, we deduce a dual magnetic description; and a slightly different duality, in the case of orthosymplectic gauge group, leads to a strong-weak coupling duality between certain supergroup Chern-Simons theories on R^3. Some cases of these statements are known in the literature. We analyze how these dualities act on line and surface operators. We also consider the purely three-dimensional version of the psu(1|1) and the U(1|1) supergroup Chern-Simons, coupled to a background complex flat gauge field. These theories compute the Reidemeister-Milnor-Turaev torsion in three dimensions. We use the 3d mirror symmetry to derive the Meng-Taubes theorem, which relates the torsion and the Seiberg-Witten invariants, for a three-manifold with arbitrary first Betti number. We also present the Hamiltonian quantization of our theories, find the modular transformations of states, and various properties of loop operators. Our results for the U(1|1) theory are in general consistent with the results, found for the GL(1|1) WZW model. We expect our findings to be useful for the construction of Chern-Simons invariants of knots and three-manifolds for more general Lie supergroups. URI: http://arks.princeton.edu/ark:/88435/dsp01zw12z768m Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: http://catalog.princeton.edu/ Type of Material: Academic dissertations (Ph.D.) Language: en Appears in Collections: Physics

Files in This Item:
File Description SizeFormat
Mikhaylov_princeton_0181D_11469.pdf1.93 MBAdobe PDF

Items in Dataspace are protected by copyright, with all rights reserved, unless otherwise indicated.