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.

arXiv comment28 pages, v3: Minor modification to match published version

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• Phases of five-dimensional supersymmetric gauge theories
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• Exact partition function in $U(2)\times U(2)$ ABJM theory deformed by mass and Fayet-Iliopoulos terms
• Exact solution of Chern-Simons-matter matrix models with characteristic/orthogonal polynomials
• 4d/2d $\to$ 3d/1d: A song of protected operator algebras
• Polynomial solution of quantum Grassmann matrices
• Mordell integrals and Giveon-Kutasov duality
• More Large $N$ limits of 3d gauge theories
• Exact results and Schur expansions in quiver Chern-Simons-matter theories
• Aspects of Massive Gauge Theories on Three Sphere in Infinite Mass Limit
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