Disorder Operators in Chern-Simons-Fermion Theories

TL;DR

This paper calculates the scaling dimensions of monopole disorder operators in Chern-Simons-fermion theories across all couplings, revealing their growth rate and implications for 3D bosonization mappings.

Contribution

It provides the first comprehensive computation of monopole operator dimensions in Chern-Simons-fermion theories at arbitrary 't Hooft coupling.

Findings

Lowest-dimension monopole operator has dimension (2/3)k^{3/2}

Results inform the understanding of fermionic disorder operators under 3D bosonization

Advances the analytic understanding of Chern-Simons-matter theories in the planar limit.

Abstract

Building on the recent progress in solving Chern-Simons-matter theories in the planar limit, we compute the scaling dimensions of a large class of disorder ("monopole") operators in $U(N)_k$ Chern-Simons-fermion theories at all 't Hooft couplings $\lambda = N/k$. We find that the lowest-dimension operator of this sort has dimension $\frac23 k^{3/2}$. We comment on the implications of these results to analyzing maps of fermionic disorder operators under 3D bosonization.