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Chern-Simons theory encoded on a spin chain

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Pérez García, David and Tierz, Miguel (2016) Chern-Simons theory encoded on a spin chain. Journal of Statistical Mechanics: Theory and Experiment . ISSN 1742-5468

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Official URL: http://iopscience.iop.org/article/10.1088/1742-5468/2016/01/013103




Abstract

We construct a one-dimensional (1D) spin chain Hamiltonian with generic interactions and prove that the thermal correlation functions of the model admit an explicit random matrix representation. As an application of the result, we show how the observables of U( N) Chern-Simons theory on S-3 can be reproduced with the thermal correlation functions of the 1D spin chain, which is of the XX type, with a suitable choice of exponentially decaying interactions between infinitely many neighbours. We show that for this model, the correlation functions of the spin chain at a finite temperature beta = 1 give the Chern-Simons partition function, quantum dimensions and the full topological S-matrix.


Item Type:Article
Uncontrolled Keywords:integrable spin chains (vertex models); matrix models; random matrix theory and extensions; gauge theories
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:36564
Deposited On:04 Apr 2016 08:27
Last Modified:09 Aug 2016 10:14

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