Supersymmetric U(N) Chern–Simons-Matter Theory and Phase Transitions

Abstract

Abstract. We study N = 2 supersymmetric U (N ) Chern-Simons with N f fundamental and N f antifundamental chiral multiplets of mass m in the parameter space spanned by (g, m, N, N f ), where g denotes the coupling constant. In particular, we analyze the matrix model description of its partition function, both at finite N using the method of orthogonal polynomials together with Mordell integrals and, at large N with fixed g, using the theory of Toeplitz determinants. We show for the massless case that there is an explicit realization of the Giveon-Kutasov duality. For finite N , with N > N f , three regimes that exactly correspond to the known three large N phases of theory are identified and characterized.

N=2∗ $$ \mathcal{N}={2}^{\ast } $$ super-Yang-Mills theory at strong coupling

“…While these are a common phenomenon in large-N theories [11,12], the behavior in N = 2 * SYM is unique and differs in many respects from phase transitions in ordinary matrix models [8]. Similar phase transitions have also been found in QCD-like vector models [8,13] as well as in three [13][14][15] and five [16] dimensional theories.…”

“…The density behaves as 15) to the right of each resonance, and approaches a finite limiting value from the left. This structure is qualitatively similar to the one previously observed at finite coupling in the vicinity of the first phase transition [8].…”

Phase transitions in 5D super Yang-Mills theory

“…As we have mentioned before there are examples of the phase transitions similar to the one we have described in this section. These are phase transitions in 3D Chern-Simons-Matter theory [30,31] and 4D super-QCD with 2N f massive hypermultiplets [24]. In both examples the phase transition of the theory in the decompactification limit at large-N is of third order.…”

“…In [30,31] authors considered matrix model obtained from the localization of N = 2 supersymmetric Chern-Simons theory on S 3 coupled to 2N f massive hypermultiplets in the fundamental representation. It was shown that in the decompactification limit this theory experiences third-order phase transition similar to the one in N = 2 SYM with 2N massive fundamental hypermultiplets on S 4 .…”

Phases of planar 5-dimensional supersymmetric Chern-Simons theory

“…However, we have also argued that there exists a series of phase transitions for increasingλ, making the existence of a supergravity dual, at the very least, problematic. Accumulating phase transitions have also appeared in 4D N = 2 * theories [37,38], 3D massive Chern-Simons theories [39,40], and mass-deformed ABJM theories [41]. Unlike the 5D pure CS model, these theories are not superconformal, still, there might be interesting connections between the different matrix models that one can explore.…”