Supersymmetry has proven to be a valuable tool in the study of non-perturbative dynamics in quantum eld theory, gravity and string theory. In this thesis we consider supersymmetric interfaces. Interfaces are defects de ned by spatially changing coupling constants. Interfaces can be used to probe the non-perturbative low energy dynamics of an underlying supersymmetric quantum eld theory. We study interfaces in a set of four-dimensional quantum eld theories with N = 2 supersymmetry known as theories of class S. Using these defects we probe the spin content of the spectrum of quantum states saturating the Bogomolnyi-Prasad-Sommerfeld bound. We also apply supersymmetric defects to the construction of knot and link invariants via quantum eld theory. We associate to a knot - presented as a tangle - an interface de ned by a spatially varying superpotential in a 2d supersymmetric Landau-Ginzburg model. We construct explicitly the Hilbert space of ground states on this interface as the cohomology of a nilpotent supercharge and prove that this Hilbert space is bi-graded by integers and is an invariant of the knot (or link). In explicit examples we show that the corresponding Poincar e polynomial coincides with the Poincar e polynomial of the renowned Khovanov homology that categori es the Jones polynomial.
Subject (authority = RUETD)
Topic
Physics and Astronomy
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Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_7418
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Form (authority = gmd)
electronic resource
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application/pdf
InternetMediaType
text/xml
Extent
1 online resource (viii, 146 p. : ill.)
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Subject (authority = ETD-LCSH)
Topic
Supersymmetry
Note (type = statement of responsibility)
by Dmitrii Galakhov
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TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
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PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
Rutgers University. Graduate School - New Brunswick
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Author Agreement License
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