Fractionally charged Wilson loops as a probe of $\theta$-dependence in $C{P}^{N-1}$ sigma models: Instantons vs. large N

Abstract

The behavior of Wilson loops with fractional charge is used to study the $\theta$-dependence of the free energy density $\epsilon (\theta )$ for the $C{P}^1$, $C{P}^5$, and $C{P}^9$ sigma models in two spacetime dimensions. The function $\epsilon (\theta )$ is extracted from the area law for a Wilson loop of charge $q=\theta /2\pi$. For $C{P}^1$, $\epsilon (\theta )$ is smooth in the region $\theta \approx \pi$ and well-described by a dilute instanton gas throughout the range $0<\theta <2\pi$. For $C{P}^5$ and $C{P}^9$ the energy exhibits a clear cusp and evidence for discrete, degenerate vacua at $\theta =\pi$, as expected from large $N$ arguments. For $C{P}^9$ the $\theta$-dependence is in good quantitative agreement with the leading order large $N$ prediction $\epsilon (\theta )=1/2{\chi }_t{\theta }^2$ throughout the range $0<\theta <\pi$.

arXiv comment16 pages, 10 figures

References in corpus (15)

• Observation of String Breaking in QCD
• Superconductors are topologically ordered
• Meron-Cluster Simulation of the $\theta$-Vacuum in the 2-d $O(3)$-Model
• Low-Dimensional Long-Range Topological Charge Structure in the QCD Vacuum
• Exploring the structure of the quenched QCD vacuum with overlap fermions
• Mass gap in the 2D O(3) non-linear sigma model with a theta=pi term
• Study of CP(N-1) θ-Vacua by Cluster-Simulation of SU(N) Quantum Spin Ladders
• Chiral Lagrangian Parameters for Scalar and Pseudoscalar Mesons
• Coherent Topological Charge Structure in $C{P}^{N-1}$ Models and QCD
• CP(N-1) Models with Theta Term and Fixed Point Action
• Critical Behavior of CP^1 at theta = pi, Haldane's Conjecture and the Universality Class
• Theta dependence of CP^9 model
• Theta-vacuum: Phase Transitions and/or Symmetry Breaking at $\theta =\pi$
• Small Instantons in $C{P}^1$ and $C{P}^2$ Sigma Models
• The $\theta$-term, CP${}^{N-1}$ Model and the Inversion Approach in the Imaginary $\theta$ Method

Cited by in corpus (8)

• Theta dependence of SU(N) gauge theories in the presence of a topological term
• Peeking into the $\theta$ vacuum
• Is $N=2$ Large?
• Theta-vacuum and large N limit in CP^{N-1} sigma models
• Anomaly Inflow and Membrane Dynamics in the QCD Vacuum
• Tachyonic crystals and the laminar instability of the perturbative vacuum in asymptotically free gauge theories
• Large $\theta$ angle in two-dimensional large $N$ ${\mathbb{CP}}^{N-1}$ model
• Anomaly Inflow and Membranes in QCD Vacuum