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.

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

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• Constraining momentum space correlators using slightly broken higher spin symmetry
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• $A_{\infty }$ Algebras from Slightly Broken Higher Spin Symmetries
• Chern-Simons dualities with multiple flavors at large $N$
• Critical Fermions with Spontaneously Broken Scale Symmetry
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• The Hilbert Space of large $N$ Chern-Simons matter theories
• Hidden sectors of Chern-Simons Matter theories and Exact Holography
• Conformal boundary conditions for a 4d scalar field
• On thermal correlators and bosonization duality in Chern-Simons theories with massive fundamental matter
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• 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