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Disorder Operators in Chern-Simons-Fermion Theories

Djordje Radicevic

TL;DR

This paper addresses the nonperturbative spectrum of disorder (monopole) operators in three-dimensional U(N)_k Chern-Simons–fermion theories in the planar limit. By evaluating the thermal partition function on $S^1_eta \times S^2_R$ in a Wu-Yang monopole background and using a double-scaling limit to access the low-temperature regime, the authors obtain the scaling dimensions of monopole states; the lowest-dimension operator with flux $q$ has $Δ = \frac{2}{3} (q\,k_{YM})^{3/2}$, with the generalization to multiple nonzero charges $Δ = \frac{2}{3} (\sum_i |q_i|^{3/2}) |k_{YM}|^{3/2}$. They discuss implications for the CS–matter bosonization duality, proposing maps to bosonic disorder operators or baryon-like composites and outlining caveats for excited monopole states. The work advances understanding of nonperturbative operator data at strong coupling and provides a framework for testing dualities beyond single-trace operators, with implications for phase structure and nonperturbative dynamics in 3D gauge theories.

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 $λ= N/k$. 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.

Disorder Operators in Chern-Simons-Fermion Theories

TL;DR

This paper addresses the nonperturbative spectrum of disorder (monopole) operators in three-dimensional U(N)_k Chern-Simons–fermion theories in the planar limit. By evaluating the thermal partition function on in a Wu-Yang monopole background and using a double-scaling limit to access the low-temperature regime, the authors obtain the scaling dimensions of monopole states; the lowest-dimension operator with flux has , with the generalization to multiple nonzero charges . They discuss implications for the CS–matter bosonization duality, proposing maps to bosonic disorder operators or baryon-like composites and outlining caveats for excited monopole states. The work advances understanding of nonperturbative operator data at strong coupling and provides a framework for testing dualities beyond single-trace operators, with implications for phase structure and nonperturbative dynamics in 3D gauge theories.

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 Chern-Simons-fermion theories at all 't Hooft couplings . We find that the lowest-dimension operator of this sort has dimension . We comment on the implications of these results to analyzing maps of fermionic disorder operators under 3D bosonization.

Paper Structure

This paper contains 6 sections, 25 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Disorder operators in three-dimensional gauge theories
  3. Monopole states in Chern-Simons-fermion theory
  4. Chern-Simons-matter in the 't Hooft limit
  5. Monopole states
  6. Outlook: new perspectives on bosonization

Figures (1)

  • Figure 1: Phases of CS-matter theories in the planar limit Jain:2013py. The red/dash-dotted line corresponds to the Gross-Witten-Wadia (GWW) phase transition Wadia:2012frGross:1980heWadia:1980cp. It intercepts $\lambda = 0$ at $\zeta = O(1)$ and is the only transition in the singlet vector model Shenker:2011zf. The blue/dashed line corresponds to the Douglas-Kazakov (DK) phase transition Douglas:1993iia. At $\lambda = 1$ there are no transitions at any $T$, in line with the assumption that this is a pure CS theory.