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Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities

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Title: Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities
Authors: Spill, Fabian
Item Type: Thesis or dissertation
Abstract: In the following dissertation, we explore the applicability of Yangian symmetry to various integrable models, in particular, in relation with S-matrices. One of the main themes in this dissertation is that, after a careful study of the mathematics of the symmetry algebras one finds that in an integrable model, one can directly reconstruct S-matrices just from the algebra. It has been known for a long time that S-matrices in integrable models are fixed by symmetry. However, Lie algebra symmetry, the Yang-Baxter equation, crossing and unitarity, which are what constrains the S-matrix in integrable models, are often taken to be separate, independent properties of the S-matrix. Here, we construct scattering matrices purely from the Yangian, showing that the Yangian is the right algebraic object to unify all required symmetries of many integrable models. In particular, we reconstruct the S-matrix of the principal chiral field, and, up to a CDD factor, of other integrable field theories with su(n) symmetry. Furthermore, we study the AdS/CFT correspondence, which is also believed to be integrable in the planar limit. We reconstruct the S-matrices at weak and at strong coupling from the Yangian or its classical limit. This version of the thesis includes minor corrections following the viva on 17 September 2010.
Issue Date: Aug-2010
Date Awarded: Dec-2010
URI: http://hdl.handle.net/10044/1/6128
DOI: https://doi.org/10.25560/6128
Supervisor: Tseytlin, Arkady
Author: Spill, Fabian
Department: Physics
Publisher: Imperial College London
Qualification Level: Doctoral
Qualification Name: Doctor of Philosophy (PhD)
Appears in Collections:Physics PhD theses

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