Pure SU Research Articles

Born-Oppenheimer potentials for SU(3) gauge theory

We develop parametrizations of eight of the lowest Born-Oppenheimer potentials for quarkonium hybrid mesons as functions of the separation r of the static quark and antiquark sources. The parameters are determined by fitting results calculated using pure SU(3) lattice gauge theory. The parametrizations have the correct limiting behavior at small r, where the potentials form multiplets associated with gluelumps. They have the correct limiting behavior at large r, where the potentials form multiplets associated with excitations of a relativistic string. There is a narrow avoided crossing in the small-r region between two potentials with the same Born-Oppenheimer quantum numbers. Published by the American Physical Society 2024

Static force from generalized Wilson loops on the lattice using the gradient flow

The static QCD force from the lattice can be used to extract ΛMS¯, which determines the running of the strong coupling. Usually, this is done with a numerical derivative of the static potential. However, this introduces additional systematic uncertainties; thus, we use another observable to measure the static force directly. This observable consists of a Wilson loop with a chromoelectric field insertion. We work in the pure SU(3) gauge theory. We use gradient flow to improve the signal-to-noise ratio and to address the field insertion. We extract ΛMS¯nf=0 from the data by exploring different methods to perform the zero-flow-time limit. We obtain the value 8t0ΛMS¯nf=0=0.629−26+22, where t0 is a flow-time reference scale. We also obtain precise determinations of several scales: r0/r1, 8t0/r0, 8t0/r1, and we compare these to the literature. The gradient flow appears to be a promising method for calculations of Wilson loops with chromoelectric and chromomagnetic insertions in quenched and unquenched configurations. Published by the American Physical Society 2024

Perturbative reheating and thermalization of pure Yang-Mills plasma

We investigate the thermalization of high-energy particles injected from the perturbative decay of inflaton during the pre-thermal phase of reheating in detail. In general, thermalization takes a relatively long time in a low-temperature plasma; therefore, the instantaneous thermalization approximation is not justified, even for the reheating of the Standard Model (SM) sector. We consider a pure Yang-Mills (YM) theory as an approximation of the SM sector or a possible dark sector, considering the Landau-Pomeranchuk-Migdal effect, a quantum interference effect in a finite temperature plasma. We perform the first numerical calculation to solve the time evolution of the system, including the redshift due to the expansion of the Universe, and show the details of the temperature evolution near the maximum and the behavior of the quasi-attractors at later times. The maximal temperature Tmax and time scale tmax are determined quantitatively, such as Tmax ≃ 0.05 × ΓIMPI2/mI32/5mI\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\left({\\Gamma}_I{M}_{\ extrm{PI}}^2/{m}_I^3\\right)}^{2/5}{m}_I $$\\end{document} and tmax ≃ 2 × 103 × ΓIMPI2/mI3−3/5mI−1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\left({\\Gamma}_I{M}_{\ extrm{PI}}^2/{m}_I^3\\right)}^{-3/5}{m}_I^{-1} $$\\end{document} in the SM-like system, where mI and ΓI are the mass and decay rate of inflaton. We also provide a similar formula for pure SU(N) and SO(N) YM theories for general values of N and coupling constant α, including Tmax ∝ α4/5 and tmax ∝ N−2α−16/5 behaviors and their numerical coefficients. The thermalization occurs in a finite time scale, resulting in a lower maximal temperature of the Universe after inflation than that under the instantaneous thermalization approximation.

Deconfinement, center symmetry and the ghost propagator in Landau gauge pure SU(3) Yang-Mills theory

The temperature dependence of the Landau gauge ghost propagator is investigated in pure SU(3) Yang-Mills theory with lattice QCD simulations. Its behavior around the confined-deconfined phase transition temperature, Tc ∼ 270 MeV, is investigated. The simulations show that in the deconfined phase, the ghost propagator is enhanced for small momenta, ≲ 1 GeV. Furthermore, the analysis of the spontaneous breaking of center symmetry on the ghost propagator is studied. Similarly as observed for the gluon propagator, the simulations result in a decoupling of the sectors where the phase of the Polyakov loop is either 0 or ±2π/3 sectors, with the latter remaining indistinguishable. The results point to the possible use of the ghost propagator as an “order parameter” for the confined-deconfined phase transition.

Rotating SU(2) gluon matter and deconfinement at finite temperature

In this work a non-abelian gauge theory is reformulated in a rotating frame. With this new formalism, the influence of the background rotation on the color deconfinement transition for a pure SU(2) gluon system has been studied. The KvBLL caloron, which is a color neutral and topologically nontrivial solution of Yang-Mills equation at finite temperature, is reexamined under rotation and adopted as the confined vacuum of such a system. With rotation-modified solutions of the caloron's constituent solitons, i.e. dyons, the non-perturbative part of effective potential of the rotating system has been obtained. Combining with the perturbative potential by Gaussian fluctuations, the critical temperature of confinement-deconfinement phase transition is investigated. It is found that neither the rotational semi-classical potential nor Gaussian fluctuations can confine color charges more tightly when the rotation becomes faster. While only a stronger coupling constant is able to make the critical temperature increase with angular velocity, as what indicated in lattice simulations. And it is found a non-monotonic dependence of the critical temperature on the angular velocity is established because of the competition between these two contrary contributions.

Description of intruder levels in the 162,164,166Dy nuclei by two different algebraic approaches

In this paper, we tried to describe both normal and intruder levels of the ground and first excited beta and gamma rotational bands of 162,164,166Dy deformed nuclei in the framework of the interacting boson model. A normal Hamiltonian of SU(3) dynamical symmetry limit is extended by adding a 2p-2 h excitation term. Also, the results are compared with the predictions of the partial dynamical symmetry for these levels of considered nuclei. The results show that, this extension removes the degeneracy suggested by the pure SU(3) symmetry and makes satisfactory agreement with the experimental counterparts for the energy levels, too. Also, a comparison between the results of this extended formalism and partial dynamical symmetry shows the advantages of the first one in the description of intruder levels, whereas the latter, makes exact results for the normal energy levels of beta and gamma energy bands. The predictions of pure SU(3), partial dynamical symmetry SU(3) and mixed formalism for different quadrupole transition rates between normal and intruder levels of this nucleus are compared with the predictions of pseudo-SU(3) model and the advantages of each model have explained in detail.

On the dynamical origin of the η′ potential and the axion mass

We investigate the dynamics responsible for generating the potential of the η′, the (would-be) Goldstone boson associated with the anomalous axial U(1) symmetry of QCD. The standard lore posits that pure QCD dynamics generates a confining potential with a branched structure as a function of the θ angle, and that this same potential largely determines the properties of the η′ once fermions are included. Here we test this picture by examining a supersymmetric extension of QCD with a small amount of supersymmetry breaking generated via anomaly mediation. For pure SU(N) QCD without flavors, we verify that there are N branches generated by gaugino condensation. Once quarks are introduced, the flavor effects qualitatively change the strong dynamics of the pure theory. For F flavors we find |N − F| branches, whose dynamical origin is gaugino condensation in the unbroken subgroup for F < N – 1, and in the dual gauge group for F > N + 1. For the special cases of F = N – 1, N, N + 1 we find no branches and the entire potential is consistent with being a one-instanton effect. The number of branches is a simple consequence of the selection rules of an anomalous U(1)R symmetry. We find that the η′ mass does not vanish in the large N limit for fixed F/N, since the anomaly is non-vanishing. The same dynamics that is responsible for the η′ potential is also responsible for the axion potential. We present a simple derivation of the axion mass formula for an arbitrary number of flavors.

Effective gravitational couplings of Kaluza-Klein gauge theories

We study the effective gravitational couplings of four-dimensional gauge theories with eight supercharges. The class of theories we analyse are arrived at via Kaluza-Klein compactification of five-dimensional gauge theories. We consider both pure SU(N) Yang-Mills theories with Chern-Simons couplings and the conformal gauge theories with 2N fundamental flavours. The resolvent of the gauge theory plays a crucial role in the calculation of these gravitational couplings. The results obtained from the Seiberg-Witten geometry are matched against independent computations using localisation.

Topology of SU(N) lattice gauge theories coupled with ℤN 2-form gauge fields

We extend the definition of Lüscher’s lattice topological charge to the case of 4d SU(N) gauge fields coupled with ℤN 2-form gauge fields. This result is achieved while maintaining the locality, the SU(N) gauge invariance, and ℤN 1-form gauge invariance, and we find that the manifest 1-form gauge invariance plays the central role in our construction. This result gives the lattice regularized derivation of the mixed ’t Hooft anomaly in pure SU(N) Yang-Mills theory between its ℤN 1-form symmetry and the θ periodicity.

Exact duality and local dynamics in SU(N) lattice gauge theory

We construct exact duality transformations in pure SU(N) Hamiltonian lattice gauge theory in ($2+1$) dimension. This duality is obtained by making a series of iterative canonical transformations on the SU(N) electric vector fields and their conjugate magnetic vector potentials on the four links around every plaquette. The resulting dual description is in terms of the magnetic scalar fields or plaquette flux loops and their conjugate electric scalar potentials. Under SU(N) gauge transformations they both transform like adjoint matter fields. The dual Hamiltonian describes the nonlocal self-interactions of these plaquette flux loops in terms of the electric scalar potentials and with inverted coupling. We show that these nonlocal loop interactions can be made local and converted into minimal couplings by introducing SU(N) auxiliary gauge fields along with new plaquette constraints. The matter fields can be included through minimal coupling. The techniques can be easily generalized to ($3+1$) dimensions.

Gravitational waves from dark SU(3) Yang-Mills theory

We analyze the phase transition in improved holographic QCD to obtain an estimate of the gravitational wave signal emitted in the confinement transition of a pure SU(3) Yang-Mills dark sector. We derive the effective action from holography and show that the energy budget and duration of the phase transition can be calculated with minor errors. These are used as input to obtain a prediction of the gravitational wave signal. To our knowledge, this is the first computation of the gravitational wave signal in a holographic model designated to match lattice data on the thermal properties of pure Yang-Mills.

Spectrum of large N glueballs: holography vs lattice

Recently there has been a notable progress in the study of glueball states in lattice gauge theories, in particular extrapolating their spectrum to the limit of large number of colors N. In this note we compare the large N lattice results with the holographic predictions, focusing on the Klebanov-Strassler model, which describes a gauge theory with mathcal{N} = 1 supersymmetry. We note that glueball spectrum demonstrates approximate universality across a range of gauge theory models. Because of this universality the holographic models can give reliable predictions for the spectrum of pure SU(N) Yang-Mills theories with and without supersymmetry. This is especially important for the supersymmetric theories, for which no firm lattice predictions exist yet, and the holographic models remain the most tractable approach. For SU(N) theories with large N the lattice non-supersymmetric and holographic supersymmetric predictions for the mass ratios of the lightest states in various sectors agree up to 5–8%, supporting the proposed universality. In particular, both lattice and holography give predictions for the 2++ and 1−− mass ratio, consistent with the known constraints on the pomeron and odderon Regge trajectories.

Schwinger–Dyson truncations in the all-soft limit: a case study

We study a special Schwinger–Dyson equation in the context of a pure SU(3) Yang–Mills theory, formulated in the background field method. Specifically, we consider the corresponding equation for the vertex that governs the interaction of two background gluons with a ghost–antighost pair. By virtue of the background gauge invariance, this vertex satisfies a naive Slavnov–Taylor identity, which is not deformed by the ghost sector of the theory. In the all-soft limit, where all momenta vanish, the form of this vertex may be obtained exactly from the corresponding Ward identity. This special result is subsequently reproduced at the level of the Schwinger–Dyson equation, by making extensive use of Taylor’s theorem and exploiting a plethora of key relations, particular to the background field method. This information permits the determination of the error associated with two distinct truncation schemes, where the potential advantage from employing lattice data for the ghost dressing function is quantitatively assessed.

Unveiling confinement in pure gauge SU(3): flux tubes, fields, and magnetic currents

A characteristic signature of quark confinement is the concentration of the chromoelectric field between a static quark–antiquark pair in a flux tube. However, the structure of this flux tube, and hence of the confining force, has not been completely understood. Here we perform new lattice measurements of field distributions on smeared Monte Carlo ensembles in SU(3) gauge theory. On the basis of these simulations we demonstrate that the confining force can be understood using the analogy with the basic principles of electromagnetism as elucidated by Maxwell. We derive a chromomagnetic Lorentz force density coupling the chromoelectric field to chromomagnetic currents and integrate this force density over the flux tube interior to obtain a Maxwell-like force that squeezes the flux tube in the transverse direction. We show that the strength of this transverse confining force is equal to the value of the string tension calculated numerically from the chromoelectric field on the midplane between the quarks, verifying the consistency of these two complementary pictures of confinement.

Holonomy saddles and 5d BPS quivers

We study the Seberg-Witten geometry of 5d mathcal{N} = 1 pure Yang-Mills theories compactified on a circle. The concept of the holonomy saddle implies that there are multiple 4d limits of interacting Seiberg-Witten theories from a single 5d theory, and we explore this in the simplest case of pure SU(N) theories. The compactification leads to N copies of locally indistinguishable 4d pure SU(N) Seiberg-Witten theories in the infrared, glued together in a manner dictated by the Chern-Simons level. We show how this picture naturally builds the 5d BPS quivers which agree with the D0 probe dynamics previously proposed via the geometrically engineered local Calabi-Yau. We work out various SU(2) and SU(3) examples through a detailed look at the respective spectral curves. We also note a special ℤ2N feature of SU(N)N spectral curves and the resulting BPS quivers, with emphasis on how the 4d holonomy saddles are affected.

Toward tensor renormalization group study of three-dimensional non-Abelian gauge theory

Abstract We propose a method to represent the path integral over gauge fields as a tensor network. We introduce a trial action with variational parameters and generate gauge field configurations with the weight defined by the trial action. We construct initial tensors with indices labelling these gauge field configurations. We perform the tensor renormalization group (TRG) with the initial tensors and optimize the variational parameters. As a first step to the TRG study of non-Abelian gauge theory in more than two dimensions, we apply this method to three-dimensional pure SU(2) gauge theory. Our result for the free energy agrees with the analytical results in the weak and strong coupling regimes.

OPE coefficients in Argyres-Douglas theories

The calculation of physical quantities in certain quantum field theories such as those of the Argyres-Douglas type is notoriously hard, due to the lack of a Lagrangian description. Here we tackle this problem following two alternative approaches. On the one hand, we use localization on the four-sphere to compute two-correlators and OPE coefficients in Argyres-Douglas superconformal theories. On the other hand, we use the conformal bootstrap machinery to put stringent bounds on such coefficients, only relying on the knowledge of central charge and conformal dimension of the operators. We compare the results obtained with these two methods and find good agreement for all rank-one cases and for the rank-two Argyres-Douglas theories (A1, A4) and (A1, A5), in the moduli space of pure SU(5) and SU(6) super Yang-Mills. We also apply our results from localization to obtain bounds on the dimensions of the lightest neutral unprotected operators of the CFTs.

Preparation of the SU(3) lattice Yang-Mills vacuum with variational quantum methods

Studying QCD and other gauge theories on quantum hardware requires the preparation of physically interesting states. The Variational Quantum Eigensolver (VQE) provides a way of performing vacuum state preparation on quantum hardware. In this work, VQE is applied to pure SU(3) lattice Yang-Mills on a single plaquette and one dimensional plaquette chains. Bayesian optimization and gradient descent were investigated for performing the classical optimization. Ansatz states for plaquette chains are constructed in a scalable manner from smaller systems using domain decomposition and a stitching procedure analogous to the Density Matrix Renormalization Group (DMRG). Small examples are performed on IBM's superconducting Manila processor.

Exact WKB and the quantum Seiberg-Witten curve for 4d N = 2 pure SU(3) Yang-Mills. Abelianization

We investigate the exact WKB method for the quantum Seiberg-Witten curve of 4d N = 2 pure SU(3) Yang-Mills in the language of abelianization. The relevant differential equation is a third-order equation on ℂℙ1 with two irregular singularities. We employ the exact WKB method to study the solutions to such a third-order equation and the associated Stokes phenomena. We also investigate the exact quantization condition for a certain spectral problem. Moreover, exact WKB analysis leads us to consider new Darboux coordinates on a moduli space of flat SL(3,ℂ)-connections. In particular, in the weak coupling region we encounter coordinates of the higher length-twist type generalizing Fenchel-Nielsen coordinates. The Darboux coordinates are conjectured to admit asymptotic expansions given by the formal quantum periods series and we perform numerical analysis supporting this conjecture.

On Emergent Particles and Stable Neutral Plasma Balls in SU(2) Yang-Mills Thermodynamics

For a pure SU(2) Yang–Mills theory in 4D, we revisit the spatial (3D), ball-like region of radius r0 in its bulk subject to the pressureless, deconfining phase at T0=1.32Tc, where Tc denotes the critical temperature for the onset of the deconfining–preconfining phase transition. Such a region possesses finite energy density and represents the self-intersection of a figure-eight shaped center-vortex loop if a BPS monopole of core radius ∼r052.4, isolated from its antimonopole by repulsion externally invoked through a transient shift of (anti)caloron holonomy (pair creation), is trapped therein. The entire soliton (vortex line plus region of self-intersection of mass m0 containing the monopole) can be considered an excitation of the pressureless and energyless ground state of the confining phase. Correcting an earlier estimate of r0, we show that the vortex-loop self-intersection region associates to the central part of a(n) (anti)caloron and that this region carries one unit of electric U(1) charge via the (electric-magnetic dually interpreted) charge of the monopole. The monopole core quantum vibrates at a thermodynamically determined frequency ω0 and is unresolved. For a deconfining-phase plasma oscillation about the zero-pressure background at T=T0, we compute the lowest frequency Ω0 within a neutral and homogeneous spatial ball (no trapped monopole) in dependence of its radius R0. For R0=r0 a comparison of Ω0 with ω0 reveals that the neutral plasma oscillates much slower than the same plasma driven by the oscillation of a monopole core.