Field Theory of Primaries in W_N Minimal Models

Abstract

For W_N minimal model CFT's at Large N, we formulate a nonlinear field theory of primary operators. A classification of single-trace operators is given first based on which an interacting field theory operating in Fock space is built. A hamiltonian is constructed with the property that it reproduces exactly the spectrum of conformal dimensions of all the primaries. This field theory is characterized by cubic (and quartic) interactions with G=1/N as an interaction parameter. It is seen that the 1/N nonlinear representation contains the interactions and structure known from Matrix-vector models.

44 pages. v4: misprints corrected, minor improvement

References in corpus (11)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Symmetries of Holographic Minimal Models
• Higher Spins in AdS and Twistorial Holography
• AdS_4/CFT_3 Construction from Collective Fields
• Quantum W-symmetry in AdS_3
• Phases of large $N$ vector Chern-Simons theories on $S^2\times S^1$
• Operator algebra of free conformal currents via twistors
• Matching four-point functions in higher spin AdS_3/CFT_2
• A semi-local holographic minimal model
• Field Theory of Primaries in W_N Minimal Models

Cited by in corpus (11)

• Higher Spins & Strings
• Large N=4 Holography
• Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation
• Matching four-point functions in higher spin AdS_3/CFT_2
• N=1 extension of minimal model holography
• Holography as a Gauge Phenomenon in Higher Spin Duality
• 1/N and Loop Corrections in Higher Spin AdS_4/CFT_3 Duality
• Field Theory of Primaries in W_N Minimal Models
• The Spectrum of Light States in Large N Minimal Models
• Chaos in Three-dimensional Higher Spin Gravity
• Higher-spin gauge theories in three spacetime dimensions