Flows, Fixed Points and Duality in Chern-Simons-matter theories

Abstract

It has been conjectured that 3d fermions minimally coupled to Chern-Simons gauge fields are dual to 3d critical scalars, also minimally coupled to Chern-Simons gauge fields. The large $N$ arguments for this duality can formally be used to show that Chern-Simons-gauged {\it critical} (Gross-Neveu) fermions are also dual to gauged `{\it regular}' scalars at every order in a $1/N$ expansion, provided both theories are well-defined (when one fine-tunes the two relevant parameters of each of these theories to zero). In the strict large $N$ limit these `quasi-bosonic' theories appear as fixed lines parameterized by $x_6$, the coefficient of a sextic term in the potential. While $x_6$ is an exactly marginal deformation at leading order in large $N$, it develops a non-trivial $\beta$ function at first subleading order in $1/N$. We demonstrate that the beta function is a cubic polynomial in $x_6$ at this order in $1/N$, and compute the coefficients of the cubic and quadratic terms as a function of the 't Hooft coupling. We conjecture that flows governed by this leading large $N$ beta function have three fixed points for $x_6$ at every non-zero value of the 't Hooft coupling, implying the existence of three distinct regular bosonic and three distinct dual critical fermionic conformal fixed points, at every value of the 't Hooft coupling. We analyze the phase structure of these fixed point theories at zero temperature. We also construct dual pairs of large $N$ fine-tuned renormalization group flows from supersymmetric $\mathcal{N}=2$ Chern-Simons-matter theories, such that one of the flows ends up in the IR at a regular boson theory while its dual partner flows to a critical fermion theory. This construction suggests that the duality between these theories persists at finite $N$, at least when $N$ is large.

arXiv comment122 pages including 6 appendices, 28 figures, 4 tables and more than 30000 words

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• 3d Abelian Gauge Theories at the Boundary
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• Momentum space parity-odd CFT 3-point functions
• Large N Renormalization Group Flows in 3d $\mathcal{N}=1$ Chern-Simons-Matter Theories
• Asymptotic safety of scalar field theories
• Constraining momentum space correlators using slightly broken higher spin symmetry
• Metastable Vacua in Large-$N$ QCD${}_3$
• Constraining momentum space CFT correlators with consistent position space OPE limit and the collider bound
• Duality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories
• Mixed three-point functions of conserved currents in three-dimensional superconformal field theory
• An all order exact result for the anomalous dimension of the scalar primary in Chern Simons Vector Models
• Fermi seas from Bose condensates in Chern-Simons matter theories and a bosonic exclusion principle
• Three-point functions of a superspin-2 current multiplet in 3D, N=1 superconformal theory
• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
• Correlation functions in $\mathcal{N}=2$ Supersymmetric vector matter Chern-Simons theory
• 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
• Charting the phase diagram of QCD${}_3$
• Crossing Symmetry in Matter Chern-Simons Theories at finite $N$ and $k$
• Mass-deformed $\mathcal{N}=3$ Supersymmetric Chern-Simons-Matter Theory
• $A_{\infty }$ Algebras from Slightly Broken Higher Spin Symmetries
• Critical Fermions with Spontaneously Broken Scale Symmetry
• Chern-Simons dualities with multiple flavors at large $N$
• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
• Hidden sectors of Chern-Simons Matter theories and Exact Holography
• 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 $N$
• Conformal boundary conditions for a 4d scalar field
• On thermal correlators and bosonization duality in Chern-Simons theories with massive fundamental matter
• QED's in $2+1$ dimensions: complex fixed points and dualities
• Chern-Simons-Matter Theories at Large Baryon Number
• Taming of preasymptotic small x evolution within resummation framework
• Four-point functions and contact terms from higher-spin Ward identities of Chern-Simons-matter theory
• 3d Large $N$ Vector Models at the Boundary
• Bifundamental Multiscalar Fixed Points in $d=3-\epsilon$
• SUSY Breaking in Monopole Quivers