Citation
Lipstein, Arthur Elias (2011) Integrability of N = 6 ChernSimons theory. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/QDSM8448. https://resolver.caltech.edu/CaltechTHESIS:05122011105136289
Abstract
In 2008, Aharony, Bergman, Jafferis, and Maldacena (ABJM) discovered a threedimensional ChernSimons theory with N = 6 supersymmetry and conjectured that in a certain limit, this theory is dual to type IIA string theory on AdS4xCP3. Since then, a great deal of evidence has been accumulated which suggests that the ABJM theory is integrable in the planar limit. Integrability is a very useful property that allows many physical observables, such as anomalous dimensions and scattering amplitudes, to be computed efficiently. In the first half of this thesis, we will explain how to use integrabilty to compute the anomalous dimensions of long, singletrace operators in the ABJM theory. In particular, we will describe how to compute them at weak coupling using a Bethe Ansatz, and how to compute them at strong coupling using string theory. The latter approach involves using algebraic curve and worldsheet techniques to compute the energies of string states dual to gauge theory operators. In the second half of this thesis, we will discuss integrability from the point of view of onshell scattering amplitudes in the ABJM theory. In particular, we will describe how to parameterize the amplitudes in terms of supertwistors and how to relate higherpoint treelevel amplitudes to lowerpoint treelevel amplitudes using a recursion relation. We will also explain how this recursion relation can be used to show that all treelevel amplitudes of the ABJM theory are invariant under dual superconformal symmetry. This symmetry is hidden from the point of the action and implies that the theory has Yangian symmetry, which is a key feature of integrability. This thesis is mainly based on the material in [94], [76], and [77].
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  integrability, ChernSimons theory, amplitudes, string theory 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Physics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Group:  Caltech Theory 
Thesis Committee: 

Defense Date:  10 May 2011 
Record Number:  CaltechTHESIS:05122011105136289 
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:05122011105136289 
DOI:  10.7907/QDSM8448 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  6387 
Collection:  CaltechTHESIS 
Deposited By:  Arthur Lipstein 
Deposited On:  17 May 2011 23:20 
Last Modified:  09 Oct 2019 17:09 
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