New phase transitions in Chern-Simons matter theory

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http://hdl.handle.net/10138/208458

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Zahabi , A 2016 , ' New phase transitions in Chern-Simons matter theory ' Nuclear Physics, Section B , vol. 903 , pp. 78-103 . DOI: 10.1016/j.nuclphysb.2015.12.003

Title: New phase transitions in Chern-Simons matter theory
Author: Zahabi, Ali
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2016-02
Language: eng
Number of pages: 26
Belongs to series: Nuclear Physics, Section B
ISSN: 0550-3213
URI: http://hdl.handle.net/10138/208458
Abstract: Applying the machinery of random matrix theory and Toeplitz determinants we study the level k, U(N) Chem-Simons theory coupled with fundamental matter on S-2 x S-1 at finite temperature T. This theory admits a discrete matrix integral representation, i.e. a unitary discrete matrix model of two-dimensional Yang Mills theory. In this study, the effective partition function and phase structure of the Chem-Simons matter theory, in a special case with an effective potential namely the Gross-Witten-Wadia potential, are investigated. We obtain an exact expression for the partition function of the Chem-Simons matter theory as a function of k, N, T, for finite values and in the asymptotic regime. In the Gross-Witten-Wadia case, we show that ratio of the Chem-Simons matter partition function and the continuous two-dimensional Yang Mills partition function, in the asymptotic regime, is the Tracy-Widom distribution. Consequently, using the explicit results for free energy of the theory, new second-order and third-order phase transitions are observed. Depending on the phase, in the asymptotic regime, Chem-Simons matter theory is represented either by a continuous or discrete two-dimensional Yang-Mills theory, separated by a third-order domain wall. (C) 2015 The Author. Published by Elsevier B.V.
Subject: ASYMPTOTICS
MODEL
111 Mathematics
114 Physical sciences
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