Scalar Correlators in Bosonic Chern-Simons Vector Models

Abstract

We consider the planar limit of Chern-Simons theories coupled to a scalar $\varphi$ in the fundamental representation of a $U(N{)}_k$ gauge group, at both the regular and Wilson-Fisher conformal points. These theories have one single-trace scalar operator $J_0={\varphi }^{†}\varphi$. We calculate its connected planar $n$-point functions, when all the external momenta are collinear. More specifically, we derive an algebraic recurrence relation that expresses each such $n$-point function in terms of lower-point ones. As an application, we study the four-point function, which was recently shown to be completely fixed up to three truncated solutions to the conformal bootstrap. We show that those truncated solutions do not contribute in our bosonic Chern-Simons theories. The result matches a recent calculation of the four-point function in Chern-Simons theories coupled to a fermion, providing a new test of 3d bosonization duality.

arXiv comment26 pages, 4 figures

References in corpus (7)

• AdS Dual of the Critical O(N) Vector Model
• Chern-Simons Theory with Vector Fermion Matter
• Higher Spin Gauge Theory and Holography: The Three-Point Functions
• Holography in 4D (Super) Higher Spin Theories and a Test via Cubic Scalar Couplings
• Supersymmetric Chern-Simons Theories with Vector Matter
• A test of bosonization at the level of four-point functions in Chern-Simons vector models
• Higher Spin de Sitter Hilbert Space

Cited by in corpus (6)

• Relation between parity-even and parity-odd CFT correlation functions in three dimensions
• Four-point functions in large $N$ Chern-Simons fermionic theories
• Duality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories
• Fermi seas from Bose condensates in Chern-Simons matter theories and a bosonic exclusion principle
• Crossing Symmetry in Matter Chern-Simons Theories at finite $N$ and $k$
• The Hilbert Space of large $N$ Chern-Simons matter theories