New Phase Transitions in Chern-Simons Matter Theory

Abstract

Applying the machinery of random matrix theory and Toeplitz determinants we study the level $k$, $U(N)$ Chern-Simons theory coupled with fundamental matter on $S^2\times S^1$ 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 Chern-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 Chern-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 Chern-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, Chern-Simons matter theory is represented either by a continuous or discrete two-dimensional Yang-Mills theory, separated by a third-order domain wall.

26 pages, 1 figure, references added, some parts rewritten and extended. To appear in Nucl. Phys. B

References in corpus (14)

• Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• The Thermal Free Energy in Large N Chern-Simons-Matter Theories
• Correlators of Large N Fermionic Chern-Simons Vector Models
• Asymptotics of Tracy-Widom distributions and the total integral of a Painlevé II function
• Phases of large $N$ vector Chern-Simons theories on $S^2\times S^1$
• ABJ Triality: from Higher Spin Fields to Strings
• Supersymmetric Chern-Simons Theories with Vector Matter
• Chern-Simons-Matter Theory
• Duality and Higher Temperature Phases of Large $N$ Chern-Simons Matter Theories on $S^2\times S^1$
• Chern-Simons-Fermion Vector Model with Chemical Potential
• Light States in Chern-Simons Theory Coupled to Fundamental Matter
• A DK Phase Transition in q-Deformed Yang-Mills on S^2 and Topological Strings
• Electrostatics of Coulomb gas, lattice paths, and discrete polynuclear growth
• Moduli space of supersymmetric QCD in the Veneziano limit

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