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Localization of Gauge Theories on the Three-Sphere


Yaakov, Itamar (2012) Localization of Gauge Theories on the Three-Sphere. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/8AMG-0B70.


We describe the application of localization techniques to the path integral for supersymmetric gauge theories in three dimensions. The localization procedure reduces the computation of the expectation value of BPS observables to a calculation in a matrix model. We describe the ingredients of this model for a general quiver gauge theory and the incorporation of supersymmetric deformations and observables.

We use the matrix model expressions to test several duality conjectures for supersymmetric gauge theories. We perform tests of mirror symmetry of three-dimensional quiver gauge theories and of Seiberg-like dualities. Specifically, we explicitly show that the partition functions of the dual pairs, which are highly nontrivial functions of the deformations, agree. We describe extensions of these dualities which can be inferred from the form of the partition functions. We review the application of the matrix model to the study of renormalization group flow and the space of conformal field theories in three dimensions.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:supersymmetry, localization
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Kapustin, Anton N.
Group:Caltech Theory
Thesis Committee:
  • Kapustin, Anton N. (chair)
  • Wise, Mark B.
  • Schwarz, John H.
  • Porter, Frank C.
Defense Date:14 May 2012
Record Number:CaltechTHESIS:05312012-204458381
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7116
Deposited By: Itamar Yaakov
Deposited On:01 Jun 2012 20:45
Last Modified:03 Oct 2019 23:56

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