Infinite N phase transitions in continuum Wilson loop operators

Abstract

We define smoothed Wilson loop operators on a four dimensional lattice and check numerically that they have a finite and nontrivial continuum limit. The continuum operators maintain their character as unitary matrices and undergo a phase transition at infinite N reflected by the eigenvalue distribution closing a gap in its spectrum when the defining smooth loop is dilated from a small size to a large one. If this large N phase transition belongs to a solvable universality class one might be able to calculate analytically the string tension in terms of the perturbative Lambda-parameter. This would be achieved by matching instanton results for small loops to the relevant large-N-universal function which, in turn, would be matched for large loops to an effective string theory. Similarities between our findings and known analytical results in two dimensional space-time indicate that the phase transitions we found only affect the eigenvalue distribution, but the traces of finite powers of the Wilson loop operators stay smooth under scaling.

31 pages, 9 figures, typos and references corrected, minor clarifications added

References in corpus (30)

• Exactly massless quarks on the lattice
• A construction of lattice chiral gauge theories
• More about exactly massless quarks on the lattice
• Aspects of Large N Gauge Theory Dynamics as Seen by String Theory
• Two Dimensional QCD is a String Theory
• Large $N$ Phase Transition in Continuum QCD${}_2$
• String Theory and Quark Confinement
• String excitation energies in SU(N) gauge theories beyond the free-string approximation
• Large N 2D Yang-Mills Theory and Topological String Theory
• Large N reduction in the continuum three dimensional Yang-Mills theory
• Does the crossover from perturbative to nonperturbative physics in QCD become a phase transition at infinite N ?
• Instanton Induced Large $N$ Phase Transitions in Two and Four Dimensional QCD
• String Effects in the Wilson Loop: a high precision numerical test
• A variant approach to the overlap action
• Unitary and Complex Matrix Models as 1-d Type 0 Strings
• The Distribution of the Largest Eigenvalue in the Gaussian Ensembles
• Chiral symmetry breaking at large N_c
• Topological Rigid String Theory and Two Dimensional QCD
• Universal Subleading Spectrum of Effective String Theory
• Asymptotic corrections to the eigenvalue density of the GUE and LUE
• Perturbation Theory for Fat-link Fermion Actions
• Instanton contributions to Wilson loops with general winding number in two dimensions and the spectral density
• Multiplying unitary random matrices - universality and spectral properties
• Strong to weak coupling transitions of SU(N) gauge theories in 2+1 dimensions
• Diffusion of Wilson Loops
• QCD_4 From a Five-Dimensional Point of View
• Large N reduction on a twisted torus
• Large-N gauge theories: lattice perspectives and conjectures
• String/Gauge Duality: (re)discovering the QCD String in AdS Space
• Phase transitions and non-analyticities in large N gauge theories

Cited by in corpus (233)

• FLAG Review 2019
• FLAG Review 2021
• High-precision scale setting in lattice QCD
• Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
• SU(N) gauge theories at large N
• Theta dependence of SU(N) gauge theories in the presence of a topological term
• An analysis of systematic effects in finite size scaling studies using the gradient flow
• The gradient flow coupling in the Schrödinger Functional
• Studying the gradient flow coupling in the Schrödinger functional
• Nonperturbative investigations of SU(3) gauge theory with eight dynamical flavors
• Symanzik improvement of the gradient flow in lattice gauge theories
• Equation of State for SU(3) Gauge Theory via the Energy-Momentum Tensor under Gradient Flow
• Large $N$ reduction with the Twisted Eguchi-Kawai model
• Gluon gravitational structure of hadrons of different spin
• Gravitational form factors of the proton from lattice QCD
• FLAG Review 2024
• Quasi parton distributions and the gradient flow
• Opportunities for Fundamental Physics Research with Radioactive Molecules
• Heavy physics contributions to neutrinoless double beta decay from QCD
• Gradient flow and scale setting on MILC HISQ ensembles
• Nonperturbative beta function of twelve-flavor SU(3) gauge theory
• Heavy quark momentum diffusion from the lattice using gradient flow
• Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\mathrm{f}}=3$ QCD
• Topological susceptibility in finite temperature (2+1)-flavor QCD using gradient flow
• Fate of the conformal fixed point with twelve massless fermions and SU(3) gauge group
• Exploring Nf=2+1 QCD thermodynamics from the gradient flow
• Nonperturbative beta function of eight-flavor SU(3) gauge theory
• Nonperturbative Renormalization of Operators in Near-Conformal Systems Using Gradient Flows
• The topological susceptibility in the large-N limit of SU(N) Yang-Mills theory
• Complex Saddles in Two-dimensional Gauge Theory
• Quark Mass Dependence of Heavy Quark Diffusion Coefficient from Lattice QCD
• Locally smeared operator product expansions in scalar field theory
• The perturbative QCD gradient flow to three loops
• Dark Matter from Strong Dynamics: The Minimal Theory of Dark Baryons
• Anisotropic pressure induced by finite-size effects in SU(3) Yang-Mills theory
• Asymptotic behavior of cutoff effects in Yang-Mills theory and in Wilson's lattice QCD
• Nonperturbative Regulator for Chiral Gauge Theories?
• $F_K/F_{\pi }$ from Möbius domain-wall fermions solved on gradient-flowed HISQ ensembles
• Eigenvalue spectra of QCD and the fate of $U_A(1)$ breaking towards the chiral limit
• Smeared quasidistributions in perturbation theory
• Finite-temperature phase structure of SU(4) gauge theory with multiple fermion representations
• Multiscale Monte Carlo equilibration: Pure Yang-Mills theory
• Extended investigation of the twelve-flavor $\beta$-function
• Correlations of Energy-Momentum Tensor via Gradient Flow in SU(3) Yang-Mills Theory at Finite Temperature
• Decay Constants of Pseudoscalar $D$-mesons in Lattice QCD with Domain-Wall Fermion
• Universality of large N phase transitions in Wilson loop operators in two and three dimensions
• ${\chi }_{\text{top}}(T\gg T_{\text{c}})$ in pure-glue QCD through reweighting
• The sphaleron rate from Euclidean lattice correlators: an exploration
• Thermodynamics in quenched QCD: energy--momentum tensor with two-loop order coefficients in the gradient flow formalism
• Heavy quark diffusion coefficient with gradient flow
• The gradient flow running coupling with twisted boundary conditions
• Lattice QCD with $N_f=2+1+1$ domain-wall quarks
• Small flow-time representation of fermion bilinear operators
• Results and techniques for higher order calculations within the gradient-flow formalism
• Repurposing lattice QCD results for composite phenomenology
• Chiral Ward identities, automatic O(a) improvement and the gradient flow
• Continuous renormalization group $\beta$ function from lattice simulations
• Thermal Heavy Quark Self-Energy from Euclidean Correlators
• The gradient flow coupling at high-energy and the scale of SU(3) Yang-Mills theory
• Four quark operators for kaon bag parameter with gradient flow
• Short flow-time coefficients of CP-violating operators
• Emergent strongly coupled ultraviolet fixed point in four dimensions with 8 Kähler-Dirac fermions
• Möbius domain-wall fermions on gradient-flowed dynamical HISQ ensembles
• Gradient-flowed thermal correlators: how much flow is too much?
• Scale setting the Möbius Domain Wall Fermion on gradient-flowed HISQ action using the omega baryon mass and the gradient-flow scales $t_0$ and $w_0$
• Non-perturbative determination of the $\Lambda$-parameter in the pure SU(3) gauge theory from the twisted gradient flow coupling
• Power corrections from decoupling of the charm quark
• Proof of the renormalizability of the gradient flow
• The renormalization group step scaling function of the 2-flavor SU(3) sextet model
• Derivation of a Gradient Flow from ERG
• Improved study of the $\beta$-function of $SU(3)$ gauge theory with $N_f=10$ massless domain-wall fermions
• A Chiral Solution to the Ginsparg-Wilson Equation
• Burgers' equation in 2D SU(N) YM
• Viscosity of pure-glue QCD from the lattice
• Quark Hadron Duality at Finite Temperature
• How perturbative are heavy sea quarks?
• Lattice determinations of the strong coupling
• The Yang-Mills gradient flow and SU(3) gauge theory with 12 massless fundamental fermions in a colour-twisted box
• Stealth dark matter confinement transition and gravitational waves
• Strong to weak coupling transitions of SU(N) gauge theories in 2+1 dimensions
• Latent heat and pressure gap at the first-order deconfining phase transition of SU(3) Yang-Mills theory using the small flow-time expansion method
• Stochastic quantisation of Yang-Mills
• Safety versus triviality on the lattice
• AdS geometry from CFT on a general conformally flat manifold
• Strong coupling constant and quark masses from lattice QCD
• Influence of topology on the scale setting
• Past, present, and future of precision determinations of the QCD coupling from lattice QCD
• Non-analyticity in scale in the planar limit of QCD
• Infrared fixed point of SU(2) gauge theory with six flavors
• Possible large-N transitions for complex Wilson loop matrices
• Gluon Green functions free of Quantum fluctuations
• Complex Burgers' equation in 2D SU(N) YM
• Using Wilson flow to study the SU(3) deconfinement transition
• Flow equation, conformal symmetry and AdS geometry
• Scale setting for large-$N$ SUSY Yang-Mills on the lattice
• Different faces of confinement
• Distribution of Energy-Momentum Tensor around a Static Quark in the Deconfined Phase of SU(3) Yang-Mills Theory
• Gradient flow exact renormalization group
• A new method for the beta function in the chiral symmetry broken phase
• Topological susceptibility in QCD with two flavors and 3-5 colors -- a pilot study
• Gradient flow and the Wilsonian renormalization group flow
• A Study of Stress-Tensor Distribution around Flux Tube in Abelian-Higgs Model
• Stochastic Renormalization Group and Gradient Flow
• Simple chromatic properties of gradient flow
• Geometries from field theories
• The Sphaleron Rate from 4D Euclidean Lattices
• 4D $\mathcal{N}=1$ SYM supercurrent in terms of the gradient flow
• Numerical computation of the beta function of large N SU(N) gauge theory coupled to an adjoint Dirac fermion
• Topology of $SU(N)$ lattice gauge theories coupled with ${\mathbb{Z}}_N$ $2$-form gauge fields
• Spectral and transport properties from lattice QCD
• Symmetries of meson correlators in high temperature QCD with physical $(u/d,s,c)$ domain-wall quarks
• Anisotropy tuning with the Wilson flow
• Rectangular Wilson Loops at Large N
• The gradient flow running coupling in SU(2) gauge theory with $N_f=8$ fundamental flavors
• A multilevel algorithm for flow observables in gauge theories
• The gradient flow in $\lambda {\varphi }^4$ theory
• QCD Static Force in Gradient Flow
• Hadronic vacuum polarization using gradient flow
• Finite temperature properties of QCD with two flavors and three, four and five colors
• Cooling Stochastic Quantization with colored noise
• Entropic order parameters in weakly coupled gauge theories
• The twisted gradient flow coupling at one loop
• Renormalization group and diffusion equation
• A novel approach to the study of conformality in the SU(3) theory with multiple flavors
• How much do charm sea quarks affect the charmonium spectrum?
• $\Lambda$ parameter of the SU(3) Yang-Mills theory from the continuous $\beta$ function
• The Yang-Mills gradient flow and lattice effective action
• Gradient flow exact renormalization group -- inclusion of fermion fields
• A large N phase transition in the continuum two dimensional SU(N) X SU(N) principal chiral model
• Topological susceptibility in finite temperature QCD with physical $(u/d,s,c)$ domain-wall quarks
• Quark masses, the Dashen phase, and gauge field topology
• On Finiteness of 2- and 3-point Functions and the Renormalisation Group
• Numerical study of tree-level improved lattice gradient flows in pure Yang-Mills theory
• Targeting the conformal window with 4+8 flavors
• Nonperturbative determination of $\beta$ functions for SU(3) gauge theories with 10 and 12 fundamental flavors using domain wall fermions
• The Wilson Flow and the finite temperature phase transition
• On the equivalence between the Wilson flow and stout-link smearing
• A second order deconfinement transition for large N 2+1 dimensional Yang-Mills theory on a small two-sphere
• Slope of the beta function at the fixed point of SU(2) gauge theory with six or eight flavors
• Lattice $B$-field correlators for heavy quarks
• Scale setting for $N_f=3+1$ QCD
• Axial U(1) current in Grabowska and Kaplan's formulation
• Setting the scale for nHYP fermions with the Lüscher-Weisz gauge action
• Supersymmetric gradient flow in the Wess-Zumino model
• Fermion number anomaly with the fluffy mirror fermion
• Chiral anomaly as a composite operator in the gradient flow exact renormalization group formalism
• Temperature Dependence of Heavy Quark Diffusion from (2+1)-flavor Lattice QCD
• Off-lightcone Wilson-line operators in gradient flow
• Short-flow-time expansion of quark bilinears through next-to-next-to-leading order QCD
• Dislocations under gradient flow and their effect on the renormalized coupling
• Renormalon-free definition of the gluon condensate within the large-${\beta }_0$ approximation
• Symanzik Improvement with Dynamical Charm: A 3+1 Scheme for Wilson Quarks
• Brief Review of Saturation Physics
• Gradient flow representation of the four-dimensional $\mathcal{N}=2$ super Yang--Mills supercurrent
• Spectroscopy of the BSM sextet model
• A Linear Equation for Wilson Loops
• Lattice QCD noise reduction for bosonic correlators through blocking
• Lattice radial quantization by cubature
• Heavy Wilson Quarks and O($a$) Improvement: Nonperturbative Results for $b_{\mathrm{g}}$
• Tunneling in two dimensional QCD
• Two Lectures on QCD at Short Distances: Jets and Factorization
• Static force from generalized Wilson loops on the lattice using the gradient flow
• Kaluza--Klein gravity & cosmology emerging from G. Perelman's entropy functionals and quantum geometric information flows
• Holographic computation of quantum corrections to the bulk cosmological constant
• Targeting the Conformal Window: Scalars on the Lattice
• Renormalization of the energy-momentum tensor in three-dimensional scalar $SU(N)$ theories using the Wilson flow
• Non-relativistic Hybrid Geometry with Gravitational Gauge-Fixing Term
• Finite continuum quasi distributions from lattice QCD
• Confinement study of an SU(4) gauge theory with fermions in multiple representations
• Machine-learned RG-improved gauge actions and classically perfect gradient flows
• HQET sum rules for matrix elements of dimension-six four-quark operators for meson lifetimes within and beyond the Standard Model
• Two dimensional fermions in four dimensional YM
• Gradient flow step-scaling function for SU(3) with $N_f$ = 6 or 4 fundamental flavors
• Wilson flow with naive staggered quarks
• Charmonium and exotics from lattice QCD
• Non-abelian lattice gauge theory with a topological action
• Beauty mesons in $N_f=2+1+1+1$ lattice QCD with exact chiral symmetry
• Precision Determination of ${\alpha }_s$ from Lattice QCD
• The two-dimensional twisted reduced principal chiral model revisited
• Schrödinger functional boundary conditions and improvement for N>3
• Dynamical solution of the strong CP problem within QCD ?
• Gradient Flow: Perturbative and Non-Perturbative Renormalization
• On the infinite gradient-flow for the domain-wall formulation of chiral lattice gauge theories
• Determination of the Strong Coupling Constant by the ALPHA Collaboration
• Symmetries of spatial correlators of light and heavy mesons in high temperature lattice QCD
• ftint: Calculating gradient-flow integrals with pySecDec
• Improved Lattice Renormalization Group Techniques
• The gradient flow of the Dirac spectrum
• Two dimensional fermions in three dimensional YM
• Continuum limit in numerical simulations of the $\mathcal{N}=2$ Landau--Ginzburg model
• A basis of the gradient flow exact renormalization group for gauge theory
• Axial $U(1)$ anomaly in a gravitational field via the gradient flow
• Holographic de Sitter Spacetime and Quantum Corrections to The Cosmological Constant
• Decoupling of charm beyond leading order
• Nonminimal gradient flows in QCD-like theories
• Latent heat and pressure gap at the first-order deconfining phase transition of SU(3) Yang-Mills theory using the small flow-time expansion method
• Large $N$ scaling and factorization in SU($N$) Yang-Mills gauge theory
• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
• The large $N$ limit of the topological susceptibility of Yang-Mills gauge theory
• Two-loop gradient-flow renormalization of scalar QCD
• Symmetries in high-temperature lattice QCD with (u, d, s, c, b) optimal domain-wall quarks
• Gradient Flow Analysis on MILC HISQ Ensembles
• Topological susceptibility and excess kurtosis in SU(3) Yang-Mills theory
• Uniqueness of gauge covariant renormalisation of stochastic 3D Yang-Mills-Higgs
• Shear and bulk viscosities of the gluon plasma across the transition temperature from lattice QCD
• Phase structure of heavy dense lattice QCD and the three-state Potts model
• A state space for 3D Euclidean Yang-Mills theories
• Applications of the Perturbative Gradient Flow
• $t\to 0$ extrapolation function in SF$t$X method for the energy-momentum tensor
• Euclidean correlation functions of the topological charge density
• Conserved vector current in QCD-like theories and the gradient flow
• Classifying Topological Charge in SU(3) Yang-Mills Theory with Machine Learning
• New $N_f=2$ Pseudofermion Action for Monte-Carlo Simulation of Lattice Field Theory with Domain-Wall Fermions
• A calculation of the gauge anomaly with the chiral overlap operator
• String tension from smearing and Wilson flow methods
• QCD static force in gradient flow
• Renormalon effect of quasi-PDF in gradient flow formalism
• Topological Susceptibility to High Temperatures via Reweighting
• Scale invariant behavior in a large N matrix model
• Remarks on correlators of Polyakov Loops
• Scale setting of SU($N$) Yang--Mills theory, topology and large-$N$ volume independence
• Matching of Wilson loop eigenvalue densities in 1+1, 2+1 and 3+1 dimensions
• Topology of the O(3) non-linear sigma model under the gradient flow
• Large N lattice gauge theory
• Estimating ${\chi }_{\mathrm{top}}$ Lattice Artifacts from Flowed SU(2) Calorons
• Taming lattice artifacts with Pauli--Villars fields
• Memory efficient finite volume schemes with twisted boundary conditions
• 4D $\mathcal{N}=1$ SYM supercurrent on the lattice in terms of the gradient flow
• Gradient-flowed order parameter for spontaneous gauge symmetry breaking
• Generalized Gradient Flow Equation and Its Applications
• The gradient flow formulation of the electroweak Hamiltonian
• Mass Spectra of $D_s$ and ${\Omega }_c$ in Lattice QCD with $N_f=2+1+1$ Domain-Wall Quarks
• Single static-quark system above $T_c$ investigated by energy-momentum tensor in SU(3) Yang-Mills theory