Citation
Willett, Brian M. (2012) Localization and Dualities in Three Dimensional Superconformal Field Theories. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/F9V6HD05. https://resolver.caltech.edu/CaltechTHESIS:05312012151945114
Abstract
In this thesis we apply the technique of localization to threedimensional N=2 superconformal field theories. We consider both theories which are exactly superconformal, and those which are believed to flow to nontrivial superconformal fixed points, for which we consider implicitly these fixed points. We find that in such theories, the partition function and certain supersymmetric observables, such as Wilson loops, can be computed exactly by a matrix model. This matrix model consists of an integral over g, the Lie algebra of the gauge group of the theory, of a certain product of 1loop factors and classical contributions. One can also consider a space of supersymmetric deformations of the partition function corresponding to the set of abelian global symmetries.
In the second part of the thesis we apply these results to test dualities. We start with the case of ABJM theory, which is dual to Mtheory on an asymptotically AdS_4xS^7 background. We extract strong coupling results in the field theory, which can be compared to semiclassical, weak coupling results in the gravity theory, and a nontrivial agreement is found. We also consider several classes of dualities between two threedimensional field theories, namely, 3D mirror symmetry, Aharony duality, and GiveonKutasov duality. Here the dualities are typically between the IR limits of two YangMills theories, which are strongly coupled in three dimensions since YangMills theory is asymptotically free here. Thus the comparison is again very nontrivial, and relies on the exactness of the localization computation. We also compare the deformed partition functions, which tests the mapping of global symmetries of the dual theories. Finally, we discuss some recent progress in the understanding of general threedimensional theories in the form of the Ftheorem, a conjectured analogy to the atheorem in four dimensions and ctheorem in two dimensions, which is closely related to the localization computation.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Quantum Field Theory; Supersymmetry; Dualities; String Theory 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Physics 
Awards:  John Stager Semple Memorial Prize in Physics, 2010 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Group:  Caltech Theory 
Thesis Committee: 

Defense Date:  15 May 2012 
Record Number:  CaltechTHESIS:05312012151945114 
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:05312012151945114 
DOI:  10.7907/F9V6HD05 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  7111 
Collection:  CaltechTHESIS 
Deposited By:  Brian Willett 
Deposited On:  01 Jun 2012 18:01 
Last Modified:  03 Oct 2019 23:56 
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