Notes on Spinning Operators in Fermionic CFT

Abstract

The Gross-Neveu model defines a unitary CFT of interacting fermions in $2<d<4$ which has perturbative descriptions in the $1/N$ expansion and in the epsilon-expansion near two and four dimensions. In each of these descriptions, the CFT has an infinite tower of nearly conserved currents of all spins. We determine the structure of the non-conservation equations both at large $N$ and in the epsilon-expansion, and use it to find the leading order anomalous dimensions of the broken currents. Similarly, we use the fact that the CFT spectrum includes a nearly free fermion to fix the leading anomalous dimensions of a few scalar composite operators. We also compute the scaling dimensions of double-trace spinning operators in the large $N$ expansion, which correspond to interaction energies of two-particle states in the AdS dual higher-spin theory. We first derive these anomalous dimensions by a direct Feynman diagram calculation, and then show that the result can be exactly reproduced by analytic bootstrap methods, provided the sum over the tower of weakly broken higher-spin currents is suitably regularized. Finally, we apply the analytic bootstrap approach to derive the anomalous dimensions of the double-trace spinning operators in the 3d bosonic and fermion vector models coupled to Chern-Simons theory, to leading order in $1/N$ but exactly in the `t Hooft coupling.

37 pages, 1 figure. v2: minor corrections

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• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Comments on operators with large spin
• Spinning AdS Propagators
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT
• Solving CFTs with Weakly Broken Higher Spin Symmetry
• TASI Lectures on the Higher Spin - CFT duality
• Revisiting the dilatation operator of the Wilson-Fisher fixed point
• Leading Order Anomalous Dimensions at the Wilson-Fisher Fixed Point from CFT
• On the AdS Higher Spin / O(N) Vector Model Correspondence: degeneracy of the holographic image
• Anomalous dimensions of leading twist conformal operators
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• Veneziano Amplitude of Vasiliev Theory
• Simplifying large spin bootstrap in Mellin space
• Anomalous Dimensions from Crossing Kernels
• Anomalous Dimensions in the WF O($N$) Model with a Monodromy Line Defect
• Revisiting the dilatation operator of the Wilson-Fisher fixed point
• Critical behavior of the QED${}_3$-Gross-Neveu-Yukawa model at four loops
• Type-B Formal Higher Spin Gravity
• Constraining momentum space correlators using slightly broken higher spin symmetry
• Double-Trace Deformations of Conformal Correlations
• Fermions in Boundary Conformal Field Theory : Crossing Symmetry and $\epsilon$-Expansion
• Test of the local form of higher-spin equations via AdS/CFT
• Scaling dimensions in QED${}_3$ from the $\epsilon$-expansion
• The epsilon expansion of the O$(N)$ model with line defect from conformal field theory
• On the Higher Spin Spectrum of Chern-Simons Theory coupled to Fermions in the Large Flavour Limit
• Towards a Bootstrap approach to higher orders of epsilon expansion
• Operator mixing in $\mathbf{\epsilon }$-expansion: scheme and evanescent (in)dependence
• Duality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories
• Slightly Broken Higher Spin Symmetry: General Structure of Correlators
• Three ways to solve critical ${\varphi }^4$ theory on $4-\epsilon$ dimensional real projective space: perturbation, bootstrap, and Schwinger-Dyson equation
• Correlation functions in $\mathcal{N}=2$ Supersymmetric vector matter Chern-Simons theory
• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
• Four point functions in CFT's with slightly broken higher spin symmetry
• Fermi seas from Bose condensates in Chern-Simons matter theories and a bosonic exclusion principle
• Critical properties of the valence-bond-solid transition in lattice quantum electrodynamics
• The large $N$ phase diagram of $\mathcal{N}=2$ $SU(N)$ Chern-Simons theory with one fundamental chiral multiplet
• Conformal Truncation of Chern-Simons Theory at Large $N_f$
• Crossing Symmetry in Matter Chern-Simons Theories at finite $N$ and $k$
• $A_{\infty }$ Algebras from Slightly Broken Higher Spin Symmetries
• Spectrum of a Gross-Neveu Yukawa model with flavor disorder in $d=3$
• The Analytic Bootstrap in Fermionic CFTs
• Chern-Simons dualities with multiple flavors at large $N$
• AdS/CFT in Fractional Dimension and Higher Spin Gravity at One Loop
• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
• Slightly broken higher-spin current in bosonic and fermionic QED in the large-$N$ limit
• Hidden sectors of Chern-Simons Matter theories and Exact Holography
• The Hilbert Space of large $N$ Chern-Simons matter theories
• Coupled minimal models revisited II: Constraints from permutation symmetry
• Anomalous dimensions of partially-conserved higher-spin currents from conformal field theory: bosonic ${\varphi }^{2n}$ theories
• The Analytic Bootstrap for Large $N$ Chern-Simons Vector Models
• On thermal correlators and bosonization duality in Chern-Simons theories with massive fundamental matter
• From Spinning Primaries to Permutation Orbifolds
• Trans-series from condensates
• Anomalous dimensions at small spins
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories
• Emergent Supersymmetry at Large $N$
• Boundary anomalous dimensions from BCFT: O($N$)-symmetric ${\varphi }^{2n}$ theories with a boundary and higher-derivative generalizations
• Correction exponents in the chiral Heisenberg model at $1/N^2$: singular contributions and operator mixing