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 S2×S1 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.