On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models

TL;DR

The paper analyzes large-N Chern-Simons vector models coupled to fundamental matter and shows that higher-spin currents j_s acquire calculable 1/N anomalous dimensions with exact λ-dependence. By combining slightly broken higher-spin symmetry constraints with classical equations of motion and direct Feynman diagram calculations, the authors derive a universal structure for the twists τ_s, τ_s−1 = (1/ÂN)[a_s λ̃^2/(1+λ̃^2) + b_s λ̃^2/(1+λ̃^2)^2] and provide explicit expressions for a_s and b_s across spins and both bosonic and fermionic theories. They also obtain parity-odd components in planar three-point functions and demonstrate consistency with the 3d bosonization duality, including strong coupling limits that match critical O(N) or Gross-Neveu models. The results are cross-validated by direct diagrammatics and align with expectations from AdS4 higher-spin duals, highlighting the robustness of the weakly broken HS framework in CS-matter theories. Overall, the work advances the quantitative understanding of HS spectra in non-supersymmetric 3d CFTs and sharpens the map between CS-vector models and their holographic duals.

Abstract

Chern-Simons gauge theories coupled to massless fundamental scalars or fermions define interesting non-supersymmetric 3d CFTs that possess approximate higher-spin symmetries at large N. In this paper, we compute the scaling dimensions of the higher-spin operators in these models, to leading order in the 1/N expansion and exactly in the 't Hooft coupling. We obtain these results in two independent ways: by using conformal symmetry and the classical equations of motion to fix the structure of the current non-conservation, and by a direct Feynman diagram calculation. The full dependence on the 't Hooft coupling can be restored by using results that follow from the weakly broken higher-spin symmetry. This analysis also allows us to obtain some explicit results for the non-conserved, parity-breaking structures that appear in planar three-point functions of the higher-spin operators. At large spin, we find that the anomalous dimensions grow logarithmically with the spin, in agreement with general expectations. This logarithmic behavior disappears in the strong coupling limit, where the anomalous dimensions turn into those of the critical O(N) or Gross-Neveu models, in agreement with the conjectured 3d bosonization duality.

Figures (7)

• Figure 1: The one-loop bulk diagrams that are expected to reproduce the $1/N$ term in the anomalous dimensions of the HS currents at the boundary.
• Figure 2: The fermion self-energy correction in the critical fermionic theory.
• Figure 3: A vertex correction in the critical fermionic theory.
• Figure 4: These two diagrams provide a third correction to the vertex in the critical fermionic theory when $s$ is even.
• Figure 5: The two-loop fermion self-energy correction.