Topological properties of $C{P}^{N-1}$ models in the large-$N$ limit

Abstract

We investigate, by numerical simulations on a lattice, the $\theta$-dependence of 2$d$ $C{P}^{N-1}$ models for a range of $N$ going from 9 to 31, combining imaginary $\theta$ and simulated tempering techniques to improve the signal-to-noise ratio and alleviate the critical slowing down of the topological modes. We provide continuum extrapolations for the second and fourth order coefficients in the Taylor expansion in $\theta$ of the vacuum energy of the theory, parameterized in terms of the topological susceptibility $\chi$ and of the so-called $b_2$ coefficient. Those are then compared with available analytic predictions obtained within the $1/N$ expansion, pointing out that higher order corrections might be relevant in the explored range of $N$, and that this fact might be related to the non-analytic behavior expected for $N=2$. We also consider sixth-order corrections in the $\theta$ expansion, parameterized in terms of the so-called $b_4$ coefficient: in this case our present statistical accuracy permits to have reliable non-zero continuum estimations only for $N\le 11$, while for larger values we can only set upper bounds. The sign and values obtained for $b_4$ are compared to large-$N$ predictions, as well as to results obtained for $SU(N_c)$ Yang-Mills theories, for which a first numerical determination is provided in this study for the case $N_c=2$.

arXiv comment14 pages, 17 eps figures

References in corpus (46)

• Simulated Tempering: A New Monte Carlo Scheme
• The QCD axion, precisely
• The QCD phase diagram for small densities from imaginary chemical potential
• Finite density QCD via imaginary chemical potential
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Critical slowing down and error analysis in lattice QCD simulations
• Scaling and Asymptotic Scaling in the SU(2) Gauge Theory
• Theta dependence of SU(N) gauge theories in the presence of a topological term
• One Loop Tests of Higher Spin AdS/CFT
• Critical slowing down of topological modes
• Comparison of the gradient flow with cooling in $SU(3)$ pure gauge theory
• Hybrid Monte Carlo and topological modes of full QCD
• The electric dipole moment of the neutron from 2+1 flavor lattice QCD
• Topology of SU(N) gauge theories at T=0 and T=Tc
• Change of theta dependence in 4D SU(N) gauge theories across the deconfinement transition
• Non-Gaussianities in the topological charge distribution of the SU(3) Yang--Mills theory
• Axion monodromy in a model of holographic gluodynamics
• Theta dependence of the deconfinement temperature in Yang-Mills theories
• Topological charge using cooling and the gradient flow
• Theta dependence of the vacuum energy in the SU(3) gauge theory from the lattice
• Instantons and the fixed point topological charge in the two-dimensional O(3) sigma-model
• $\theta$ dependence of 4D $SU(N)$ gauge theories in the large-$N$ limit
• $\theta$ dependence in $SU(3)$ Yang-Mills theory from analytic continuation
• Phase diagram of Yang-Mills theories in the presence of a theta term
• The topological susceptibility in the large-N limit of SU(N) Yang-Mills theory
• Corrections to Finite-Size Scaling in the Lattice N-Vector Model for Infinite N
• Theta-dependence of the spectrum of SU(N) gauge theories
• The 4D SU(3) gauge theory with an imaginary theta term
• Field theoretical approach to the study of theta dependence in Yang-Mills theories on the lattice
• Fighting topological freezing in the two-dimensional CP${}^{N-1}$ model
• Topological critical slowing down: variations on a toy model
• Topological susceptibility and string tension in the lattice CP(N) models
• Metadynamics Surfing on Topology Barriers: the $C{P}^{N-1}$ Case
• Notes on Theta Dependence in Holographic Yang-Mills
• $\theta$ dependence in trace deformed $SU(3)$ Yang-Mills theory: a lattice study
• Monte Carlo simulation of lattice ${\mathrm{CP}}^{N-1}$ models at large N
• Topology in 2D CP**(N-1) models on the lattice: a critical comparison of different cooling techniques
• Behavior near $\theta =\pi$ of the mass gap in the 2D O(3) non-linear sigma model
• On Statistical Mechanics of Instantons in the CP^{N_c-1} Model
• Renormalization group flow and fixed point of the lattice topological charge in the 2-d O(3) sigma-model
• On the effective Lagrangian of CP^(N-1) models in the large N limit
• Theta-vacuum and large N limit in CP^{N-1} sigma models
• Small Instantons in $C{P}^1$ and $C{P}^2$ Sigma Models
• Worm Algorithm for CP(N-1) Model
• The effects of quantum instantons on the thermodynamics of the CP^(N-1) model
• Numerical Evidence for the Haldane Conjecture

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• Towards glueball masses of large-$N$ $\mathrm{SU}(N)$ pure-gauge theories without topological freezing
• Large-$N$ $SU(N)$ Yang-Mills theories with milder topological freezing
• Large-$N$ expansion and $\theta$-dependence of $2d$ $C{P}^{N-1}$ models beyond the leading order
• $\theta$-dependence and center symmetry in Yang-Mills theories
• The Large $N_c$ limit of QCD on the lattice
• The topological susceptibility of two-dimensional $U(N)$ gauge theories
• Confinement-Deconfinement Crossover in the Lattice $\mathbb{C}{P}^{N-1}$ Model
• Lattice $\mathbb{C}{P}^{N-1}$ model with ${\mathbb{Z}}_N$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy
• Is $N=2$ Large?
• Lattice determination of the topological susceptibility slope ${\chi }^{\prime }$ of $2d{\mathrm{CP}}^{N-1}$ models at large $N$
• Ground state modulations in the $\mathbb{C}{P}^{N-1}$ model
• Fractional topological charge in $SU(N)$ gauge theories without dynamical quarks
• Two-dimensional multicomponent Abelian-Higgs lattice models
• Topological susceptibility of $2d{\mathrm{CP}}^1$ or $\mathrm{O}(3)$ non-linear $\sigma$-model: is it divergent or not?
• $\theta$-dependence in the small-$N$ limit of $2d$ $C{P}^{N-1}$ models
• Large-$N$ ${\mathbb{CP}}^{N-1}$ sigma model on a Euclidean torus: uniqueness and stability of the vacuum
• Remarks on the large-$N$ $\mathbb{C}{P}^{N-1}$ model
• Large $\theta$ angle in two-dimensional large $N$ ${\mathbb{CP}}^{N-1}$ model