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RUcore Resource Object
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TitleBergman kernel, balanced metrics and black holes
NameKlevtsov, Semyon (author), Douglas, Michael (chair), Schentzer, Steve (internal member), Lukyanov, Sergei (internal member), Langreth, David (internal member), Phong, Duong (outside member), Rutgers University, Graduate School - New Brunswick,
Degree Date2009-10
Date Created2009
SubjectPhysics and Astronomy,
Bergman kernel functions,
Black holes (Astronomy)
DescriptionIn this thesis we explore the connections between the Kahler geometry and Landau levels on compact manifolds. We rederive the expansion of the Bergman kernel on Kahler manifolds developed by Tian, Yau, Zelditch, Lu and Catlin, using path integral and perturbation theory. The physics interpretation of this result is as an expansion of the projector of wavefunctions on the lowest Landau level, in the special case that the magnetic field is proportional to the Kahler form. This is a geometric expansion, somewhat similar to the DeWitt-Seeley-Gilkey short time expansion for the heat kernel, but in this case describing the long time limit, without depending on supersymmetry. We also generalize this expansion to supersymmetric quantum mechanics and more general magnetic fields, and explore its applications. These include the quantum Hall effect in curved space, the balanced metrics and Kahler gravity. In particular, we conjecture that for a probe in a BPS black hole in type II strings compactified on Calabi-Yau manifolds, the moduli space metric is the balanced metric.
NotePh.D.
NoteIncludes bibliographical references (p. 75-80)
Noteby Semyon Klevtsov
Genretheses
Persistent URLhttp://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000051849
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