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Refined BPS invariants, Chern-Simons theory, and the quantum dilogarithm

Citation

Dimofte, Tudor Dan (2010) Refined BPS invariants, Chern-Simons theory, and the quantum dilogarithm. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:05142010-131147918

Abstract

In this thesis, we consider two main subjects: the refined BPS invariants of Calabi-Yau threefolds, and three-dimensional Chern-Simons theory with complex gauge group. We study the wall-crossing behavior of refined BPS invariants using a variety of techniques, including a four-dimensional supergravity analysis, statistical-mechanical melting crystal models, and relations to new mathematical invariants. We conjecture an equivalence between refined invariants and the motivic Donaldson-Thomas invariants of Kontsevich and Soibelman. We then consider perturbative Chern-Simons theory with complex gauge group, combining traditional and novel approaches to the theory (including a new state integral model) to obtain exact results for perturbative partition functions. We thus obtain a new class of topological invariants, which are not of finite type, defined in the background of genuinely nonabelian flat connections. The two main topics, BPS invariants and Chern-Simons theory, are connected at both a formal and (we believe) deeper conceptual level by the striking central role that the quantum dilogarithm function plays in each.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:String theory, Chern-Simons theory, BPS invariants
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Gukov, Sergei (advisor)
  • Ooguri, Hirosi (co-advisor)
Thesis Committee:
  • Gukov, Sergei (chair)
  • Ooguri, Hirosi (co-chair)
  • Schwarz, John H.
  • Calegari, Danny C.
Defense Date:30 April 2010
Author Email:tdd (AT) theory.caltech.edu
Record Number:CaltechTHESIS:05142010-131147918
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:05142010-131147918
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5808
Collection:CaltechTHESIS
Deposited By: Tudor Dan Dimofte
Deposited On:21 May 2010 16:20
Last Modified:26 Dec 2012 03:25

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