Supersymmetric $U(N)$ Chern-Simons-matter theory and phase transitions

Abstract

We study $\mathcal{N}=2$ supersymmetric $U(N)$ Chern-Simons with $N_f$ fundamental and $N_f$ antifundamental chiral multiplets of mass $m$ in the complete 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.

28 pages, v3: Minor modification to match published version

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• The 4d Superconformal Index from q-deformed 2d Yang-Mills
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Cited by in corpus (7)

• N=2* Super-Yang-Mills Theory at Strong Coupling
• Transmutation of a Trans-series: The Gross-Witten-Wadia Phase Transition
• Phases of planar 5-dimensional supersymmetric Chern-Simons theory
• 4d/2d $\to$ 3d/1d: A song of protected operator algebras
• Phase structure of $\mathcal{N}=2^{\ast }$ SYM on ellipsoids
• Phase transitions in 5D super Yang-Mills theory
• Self-reciprocal functions and double Mordell integrals