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

TL;DR

This paper calculates the scaling dimensions of higher-spin operators in large N Chern-Simons vector models, revealing how these dimensions depend on the coupling and relate to dualities with other 3d models.

Contribution

It provides exact leading-order results for higher-spin operator dimensions in Chern-Simons matter theories, using conformal symmetry and diagrammatic methods, and explores their behavior across coupling regimes.

Findings

Anomalous dimensions grow logarithmically with spin at large spin.

Disappearance of logarithmic growth at strong coupling.

Results support 3d bosonization duality.

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.