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Interfaces in supersymmetric field theories
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Galakhov, Dmitrii. Interfaces in supersymmetric field theories. Retrieved from https://doi.org/doi:10.7282/T3PC34Q9

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TitleInterfaces in supersymmetric field theories
NameGalakhov, Dmitrii (author); Moore, Gregory Winthrop (chair); Halkiadakis, Eva (internal member); Diaconescu, Duiliu Emanuel (internal member); Goldstein, Sheldon (internal member); Aganagic, Mina (outside member); Rutgers University; Graduate School - New Brunswick
Date Created2016
Other Date2016-10 (degree)
SubjectPhysics and Astronomy, Supersymmetry
Extent1 online resource (viii, 146 p. : ill.)
DescriptionSupersymmetry 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.
NotePh.D.
NoteIncludes bibliographical references
Noteby Dmitrii Galakhov
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T3PC34Q9
Languageeng
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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