Duality and Higher Temperature Phases of Large $N$ Chern-Simons Matter Theories on $S^2\times S^1$

Abstract

It has been recently demonstrated that the thermal partition function of any large $N$ Chern-Simons gauge theories on $S^2$, coupled to fundamental matter, reduces to a capped unitary matrix model. The matrix models corresponding to several specific matter Chern-Simons theories at temperature $T$ were determined in arXiv:1301.6169. The large $N$ saddle point equations for these theories were determined in the same paper, and were solved in the low temperature phase. In this paper we find exact solutions for these saddle point equations in three other phases of these theories and thereby explicitly determine the free energy of the corresponding theories at all values of $T^2/N$. As anticipated on general grounds in arXiv:1301.6169, our results are in perfect agreement with conjectured level rank type bosonization dualities between pairs of such theories.

62 pages, 20 figures, minor changes, published version

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• On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models
• Unitarity, Crossing Symmetry and Duality of the S-matrix in large N Chern-Simons theories with fundamental matter
• Disorder Operators in Chern-Simons-Fermion Theories
• Flows, Fixed Points and Duality in Chern-Simons-matter theories
• Unitarity, Crossing Symmetry and Duality in the scattering of $\mathcal{N}=1$ Susy Matter Chern-Simons theories
• Chern Simons Bosonization along RG Flows
• Poles in the $S$-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics
• Superspace formulation and correlation functions of 3d superconformal field theories
• Constraining momentum space correlators using slightly broken higher spin symmetry
• Scattering Amplitude and Bosonization Duality in General Chern-Simons Vector Models
• All tree level scattering amplitudes in Chern-Simons theories with fundamental matter
• Large N Chern-Simons with massive fundamental fermions - A model with no bound states
• Chern-Simons-Ghost Theories and de Sitter Space
• Line Operators in Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• Bose-Fermi Chern-Simons Dualities in the Higgsed Phase
• Dense Chern-Simons Matter with Fermions at Large N
• Duality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories
• Chern-Simons theory coupled to bifundamental scalars
• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
• Dual Superconformal Symmetry of $\mathcal{N}=2$ Chern-Simons theory with Fundamental Matter at Large $N$
• Fermi seas from Bose condensates in Chern-Simons matter theories and a bosonic exclusion principle
• Correlation functions in $\mathcal{N}=2$ Supersymmetric vector matter Chern-Simons theory
• Testing the Boson/Fermion Duality on the Three-Sphere
• Matter Chern Simons Theories in a Background Magnetic Field
• Anyonic correlation functions in Chern-Simons matter theories
• The large $N$ phase diagram of $\mathcal{N}=2$ $SU(N)$ Chern-Simons theory with one fundamental chiral multiplet
• Mass-deformed $\mathcal{N}=3$ Supersymmetric Chern-Simons-Matter Theory
• Crossing Symmetry in Matter Chern-Simons Theories at finite $N$ and $k$
• From Phase Space to Integrable Representations and Level-Rank Duality
• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
• The Hilbert Space of large $N$ Chern-Simons matter theories
• Scattering Amplitudes in $\mathcal{N}=3$ Supersymmetric $SU(N)$ Chern-Simons-Matter Theory at Large $N$
• Hidden sectors of Chern-Simons Matter theories and Exact Holography
• New Phase Transitions in Chern-Simons Matter Theory
• On thermal correlators and bosonization duality in Chern-Simons theories with massive fundamental matter
• Chern-Simons theory encoded on a spin chain
• Roton-phonon excitations in Chern-Simons matter theory at finite density
• Large N Thirring Matter in Three Dimensions
• Emergent Supersymmetry at Large $N$
• Three Dimensional Bosonization From Supersymmetry