Arata Yamamoto
We perform the Monte Carlo study of the SU(3) non-Abelian Higgs model. We discuss phase structure and non-Abelian vortices by gauge invariant operators. External magnetic fields induce non-Abelian vortices in the color-flavor locked phase. The spatial distribution of non-Abelian vortices suggests the repulsive vortex-vortex interaction.
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We study Abelian monopole and vortex condensation in lattice pure gauge theories. Condensation is detected by means of a disorder parameter defined in terms of a gauge-invariant effective action introduced using the lattice Schrödinger functional. Dirac monopoles condense in the confined phase of U(1) lattice gauge theory. Abelian monopoles and Abelian vortices condense in the confined phase of SU(2) and SU(3) lattice gauge theories.
We study the condensation of Abelian and Center vortices in SU(3) lattice gauge theory at finite temperature. We find that both vortices condense in the confined phase of the SU(3) vacuum.
We consider full non-Abelian, Abelian and center projected lattice field configurations built up from random instanton gas configurations in the continuum. We study the instanton contribution to the $\bar{Q}Q$ force with respect to ({\it i}) instanton density dependence, ({\it ii}) Casimir scaling and ({\it iii}) whether various versions of Abelian dominance hold. We check that the dilute gas formulation for the interaction potential gives an reliable approximation only for densities small compared to the phenomenological value. We find that Casimir scaling does not hold, confirming earlier st…
We present evidence that the center vortex model of confinement is more consistent with lattice results than other currently available models. In particular we show that Abelian field distributions predicted by monopole plasma, caloron gas or dual superconductor models cannot reproduce the area-law falloff of double winding Wilson loops in full $SU(2)$ and center vortex only gauge fields.
The non-compact lattice version of the Abelian Higgs model is studied in terms of its topological excitations. The Villain form of the partition function is represented as a sum over world-sheets of gauge-invariant ``vortex'' strings. The phase transition of the system is then related to the density of these excitations. Through Monte Carlo simulations the density of the vortex sheets is shown to be a good order parameter for the system. The vortex density essentially vanishes in the Higgs phase, and the Coulomb phase consists of a single vortex condensate.
We report on a breakdown of both monopole dominance and positivity in abelian-projected lattice Yang-Mills theory. The breakdown is associated with observables involving two units of the abelian charge. We find that the projected lattice has at most a global $Z_2$ symmetry in the confined phase, rather than the global U(1) symmetry that might be expected in a dual superconductor or monopole Coulomb gas picture. Implications for monopole and center vortex theories of confinement are discussed.
The confining and topological properties of the compact Abelian Higgs model with doubly-charged Higgs field in three space-time dimensions are studied. We consider the London limit of the model. We show that the monopoles are forming chain-like structures (kept together by ANO vortices) the presence of which is essential for getting simultaneously permanent confinement of singly-charged particles and breaking of the string spanned between doubly-charged particles. In the confinement phase the chains are forming percolating clusters while in the deconfinement (Higgs) phase the chains are of fin…
We present the first measurement of the vortex free-energy order parameter at weak coupling for SU(2) in simulations employing multihistogram methods. The result shows that the excitation probability for a sufficiently thick vortex in the vacuum tends to unity. This is rigorously known to provide a necessary and sufficient condition for maintaining confinement at weak coupling in SU(N) gauge theories.
We discuss the abelian vortex dynamics in the abelian projection approach to non-abelian spin models. We show numerically that in the three-dimensional SU(2) spin model in the Maximal Abelian projection the abelian off-diagonal vortices are not responsible for the phase transition contrary to the diagonal vortices. A generalization of the abelian projection approach to SU(N) spin models is briefly discussed.
In the context of softly broken N=2 supersymmetric quantum chromodynamics (SQCD), with a hierarchical gauge symmetry breaking SU(N+1) -> U(N) -> 1, at scales v1 and v2, respectively, where v1 >> v2, we construct monopole-vortex complex soliton-like solutions and examine their properties. They represent the minimum of the static energy under the constraint that the monopole and antimonopole positions sitting at the extremes of the vortex are kept fixed. They interpolate the 't Hooft-Polyakov-like regular monopole solution near the monopole centers and a vortex solution far from them and in betw…
Numerical data for the SU(2) confining string in the maximal abelian projection are analysed. The distribution of the electric flux and monopole currents are perfectly described by the classical equations of motion for the dual Abelian Higgs model. The mass of the vector boson is equal to the mass of the monopole (Higgs particle) within numerical errors. The classical energy per unit length of the Abrikosov vortex reproduces 94% of the full non-Abelian string tension.
We discuss a new approach to the investigation of the nature of the mass gap in spin systems with continuous global symmetries which is much analogous to the method of abelian projection in the gauge theories. We suggest that the abelian degrees of freedom, in particular, abelian vortices are responsible for the mass gap generation phenomena in the non-abelian spin systems. To check our hypothesis we study numerically the three-dimensional SU(2) spin model in the Maximal Abelian projection. We find that the abelian mass gap in the projected theory coincides with the full non-abelian mass gap w…
We find that Polyakov lines, computed in abelian-projected SU(2) lattice gauge theory in the confined phase, have finite expectation values for lines corresponding to two units of the abelian electric charge. This means that the abelian-projected lattice has at most Z(2), rather than U(1), global symmetry. We also find a severe breakdown of the monopole dominance approximation, as well as positivity, in this charge-2 case. These results imply that the abelian-projected lattice is not adequately represented by a monopole Coulomb gas; the data is, however, consistent with a center vortex structu…
We describe a new order parameter for the confinement-deconfinement transition in lattice SU(2) Yang-Mills theory. It is expressed in terms of magnetic monopole field correlators represented as sums over sheets of center vortices. Our construction establishes a link between "abelian" and "center dominance". It avoids an inconsistency in the treatment of small scales present in earlier definitions of monopole fields by respecting Dirac's quantization condition for magnetic fluxes.
In SU(2) lattice gauge theory, a new self-restricted cooling procedure is developed to uncover the gauge invariant vortex vacuum texture. The emerging vortex vacuum structure amounts to the full string tension and gives rise to a mass dimension four condensate which is of pure vortex origin.
For SU(2) lattice gauge theory, a new SO(3) cooling procedure is proposed which removes the SU(2)/Z(2) coset fields from the lattice configurations and reveals a Z(2) vortex vacuum texture different from the P-vortex content obtained in the maximal center gauge. Cooling can be restricted in a renormalization group invariant way by a parameter controlling the remaining SO(3) action density. A gauge invariant Z(2) vortex vacuum emerges asymptotically if cooling is not restricted. This ``vortex texture'' does not support the string tension or a finite part of it. The SU(2) action density associat…
A new algorithm for fixing the gauge to (direct) maximal center gauge in SU(N) lattice gauge theory is presented. We check how this method works on SU(3) configurations which are vortex-like, and show how these configurations look like when center projected.
We argue that the ``vortex-finding'' property of maximal center gauge, i.e. the ability of this gauge to locate center vortices inserted by hand on any given lattice, is the key to its success in extracting the vortex content of thermalized lattice configurations. We explain how this property comes about, and why it is expected not only in maximal center gauge, but also in an infinite class of gauge conditions based on adjoint-representation link variables. In principle, the vortex-finding property can be foiled by Gribov copies. This fact is relevant to a gauge-fixing procedure devised by Kov…
We introduce quantum gauge fixing (QGF) as a new class of gauge fixings. While the maximal center gauge might not show vortex dominance, the confining properties of the vortices observed in past lattice calculations are argued to have been obtained in a gauge more akin to QGF than to the strict maximal center gauge.
We study how Laplacian Center Gauge identifies the vortex content of a thick SU(2) vortex configuration on the lattice. This configuration is a solution of the Yang-Mills classical equations of motion having vortex properties. We find that this gauge fixing procedure cleanly identifies the underlying vortex properties. We also study the monopole content of this configuration detected with this procedure. We obtain two monopole curves lying on the surface of the vortex.
We examine the formation of vortices during the nonequilibrium relaxation of a high-temperature initial state of an Abelian-Higgs system. We equilibrate the scalar and gauge fields using gauge-invariant Langevin equations and relax the system by instantaneously removing thermal fluctuations. For couplings near critical we observe the formation of large clusters of like-sign magnetic vortices. Their appearance has implications for the dynamics of the phase transition, for the observed distribution of topological defects and for late-time phase ordering kinetics. We offer explanations for both t…
Resorting to the the Laplace center gauge (LCG) and to the Maximal-center gauge (MCG), respectively, confining vortices are defined by center projection in either case. Vortex properties are investigated in the continuum limit of SU(2) lattice gauge theory. The vortex (area) density and the density of vortex crossing points are investigated. In the case of MCG, both densities are physical quantities in the continuum limit. By contrast, in the LCG the piercing as well as the crossing points lie dense in the continuum limit. In both cases, an approximate treatment by means of a weakly interactin…
We present a new way of fixing the gauge to (direct) maximal center gauge in SU(N) Yang-Mills theory and apply this method to SU(3) configurations which are vortex-like. We study the structure of the Z_3 configurations obtained after center-projecting the SU(3) ones.
We study the application of $\mathrm{SU}(3)$ gauge field smoothing methods to $\mathrm{Z}(3)$-projected center-vortex gauge fields. Due to the proportionality of the vortex links to the identity, naive applications of these methods are either ineffectual or limited in scope, containing subtle issues which are not obviously manifest. To overcome these issues we introduce centrifuge preconditioning, a novel method applied prior to smoothing that rotates the links away from the center while preserving the fundamental structure of the vortex field. Additionally, the concept of vortex-preserved ann…
The magnetic vortices which arise in SU(2) lattice gauge theory in center projection are visualized for a given time slice. We establish that the number of vortices piercing a given 2-dimensional sheet is a renormalization group invariant and therefore physical quantity. We find that roughly 2 vortices pierce an area of 1 fm^2.
Lattice gauge theories with gauge groups SO(3) and SU(2) are compared. The free energy of electric twist, an order parameter for the confinement-deconfinement transition which does not rely on centre-symmetry breaking, is measured in both theories. The results are used to calibrate the scale in SO(3).
Using the renormalization group motivated smoothing technique, the large scale structure of lattice configurations at finite temperature is characterized in terms of Abelian monopoles identified in the maximally Abelian, the Laplacian Abelian, and the Polyakov gauge. Abundance and anisotropy of monopoles at deconfinement and gauge invariant properties like local non-Abelian action and topological density are studied. Monopoles are predominantly found in regions of large action and topological charge, rather independent of the chosen gauge.
The random vortex world-surface model is extended to the gauge groups SU(4) and Sp(2). Compared to the SU(2) and SU(3) models studied previously, which reproduce the infrared properties of the corresponding Yang-Mills theories on the basis of a simple vortex world-surface curvature action, new dynamical characteristics become important. In the SU(4) case, an explicit dependence of the vortex effective action on the configuration of the Abelian magnetic monopoles residing on the vortices emerges; in the Sp(2) case, a new "stickiness" contribution to the vortex action serves to drive the deconfi…
The vortex theory which emerges from SU(2) lattice gauge theory by center projection is briefly reviewed. In this vortex picture, quark confinement is due to percolating (closed) vortices which are randomly linked to the Wilson loop. The deconfinement phase transition appears as a de-percolation phase transition.
We study the stability of Z_2 topological vortex excitations in d+1 dimensional SU(2) Yang-Mills theory on the lattice at T=0. This is found to depend on d and on the coupling considered. We discuss the connection with lattice artifacts causing bulk transitions in the beta_A-beta_F plane and draw some conclusions regarding the continuum limit of the theory.
We perform lattice Monte-Carlo simulations of pure SU(2) QCD using the multi-level method. We find Abelian dominance in local unitary gauges such as those diagonalizing a plaquette. A static potential described by Abelian link fields alone gives us the same string tension as that of a non-Abelian potential. Abelian dominance of the string tension and Abelian flux tube profiles are observed also without gauge-fixing, i.e., without any Abelian projection. On the basis of these results, we propose a simple gauge-independent Abelian confinement scenario without any Abelian projection. All color co…
We gauge fix 600 SU(3) beta=6.0 configurations on a 16^4 lattice to a simple form of the maximal abelian gauge. We project the SU(3) valued links to the U(1)xU(1) subgroup, and extract U(1)xU(1) and monopole string tensions. After gauge fixing to the indirect center gauge, the U(1)xU(1) links are projected to Z(3) and a vortex string tension is measured. The vortex and magnetic current densities are measured.
We explore simulations on periodic lattices in the Tomboulis $SO(3) \times Z(2)$ formulation. We measure gauge invariant vortex counters for "thin", "thick" and "hybrid" vortex sheets in order to tag Wilson loops by the occurance of gauge invariant vortices linking them. We also measure projection vortex counters defined in the maximal center gauge for comparison.
Propagators of the diagonal and the off-diagonal gluons are studied numerically in the Maximal Abelian gauge of SU(2) lattice gauge theory. It is found that in the infrared region the propagator of the diagonal gluon is strongly enhanced in comparison with the off--diagonal one. The enhancement factor is about 50 at our smallest momentum 325 MeV. We have also applied various fits to the propagator formfactors.
We formulate a stochastic gauge fixing method to study the gauge dependence of the Abelian projection. We consider a gauge which interpolates between the maximal Abelian gauge and no gauge fixing. We have found that Abelian dominance for the heavy quark potential holds even in a gauge which is far from maximally Abelian one. The heavy quark potentials from monopole and photon contribution are calculated at several values of the gauge parameter, and the former part shows always the confinement behavior.
We introduce a generalized Maximum Abelian Gauge (MAG). We work with this new gauge on 12^4 lattices for beta=5.7,5.8 and 16^4 lattices for beta=5.9,6.0. We also introduce a form of abelian projection related to the generalized MAG. We measure U(1)xU(1) wilson loops and single color magnetic current densities.
Chiral symmetry breaking parameters are calculated in quenched SU(2) gauge theory and with Abelian gauge fields projected in maximal Abelian gauge and in field strength gauge. Maximal Abelian gauge projected fields lead to chiral condensate values which are quite similar to those of the full nonabelian theory. Pseudoscalar and vector meson correlators are calculated and found to be reproduced by the use of maximal Abelian gauge fields for small quark masses. In field-strength gauge, Abelian-projected fields give a chiral condensate which closely resembles the results of strongly coupled ($β<1$…
The c-vortex ensembles are constructed by means of the recently proposed cooling method which gradually removes the SU(2)/Z_2 coset fields from the SU(2) lattice configurations and which thus reveals the Z_2 vortex vacuum texture. Using Teper's blocking method, the screening masses of the 0+ and the 2+ glueball is calculated from these vortex ensembles and compared with the masses obtained from full configurations. The masses of either case agree within the achieved numerical accuracy of 10%. As a byproduct, we find that the overlaps of the Teper operators with the glueball wavefunctions are s…
The center vortex model of quantum chromodynamic states that vortices, closed color-magnetic flux, percolate the vacuum. Vortices are seen as the relevant excitations of the vacuum, causing confinement and dynamical chiral symmetry breaking. In an appropriate gauge, as \textit{direct maximal center gauge}, vortices are detected by projecting onto the center degrees of freedom. Such gauges suffer from Gribov copy problems: different local maxima of the corresponding gauge functional can result in different predictions of the string tension. By using non-trivial center regions, that is, regions …
We present results for the fundamental string tension in SU(2) lattice gauge theory after projection to maximal abelian and direct maximal center gauges. We generate 20 Gribov copies/configuration. Abelian and center projected string tensions slowly decrease as higher values of the gauge functionals are reached.
The structures of confining vortices which underlie pure SU(3) Yang-Mills theory are studied by means of lattice gauge theory. Vortices and Z_3 monopoles are defined as dynamical degrees of freedom of the Z_3 gauge theory which emerges by center gauge fixing and by subsequent center projection. It is observed for the first time for the case of SU(3) that these degrees of freedom are sensible in the continuum limit: the planar vortex density and the monopole density properly scales with the lattice spacing. By contrast to earlier findings concerning the gauge group SU(2), the effective vortex t…
The important role of centre vortices in dynamical chiral symmetry breaking and corresponding dynamical mass generation has been demonstrated in pure gauge studies of the Landau-gauge quark propagator. We present initial results of our investigation into the impact of centre vortex removal on the Landau-gauge propagator on dynamical gauge fields. To ensure sensitivity to the topology of the gauge fields, the propagator is computed with overlap fermions. Upon removal of centre vortices we find that dynamical mass generation is suppressed. The quark renormalisation function remains remarkably fl…
We study magnetic flux tubes in the Higgs vacuum of the N=1^* mass deformation of SU(N_c), N=4 SYM and its large N_c string dual, the Polchinski-Strassler geometry. Choosing equal masses for the three adjoint chiral multiplets, for all N_c we identify a "colour-flavour locked" symmetry, SO(3)_{C+F} which leaves the Higgs vacuum invariant. At weak coupling, we find explicit non-Abelian k-vortex solutions carrying a Z_{N_c}-valued magnetic flux, with winding, 0 < k < N_c. These k-strings spontaneously break SO(3)_{C+F} to U(1)_{C+F} resulting in an S^2 moduli space of solutions. The world-sheet …
We present an algorithm for simulation of $SU(2)$ lattice gauge theory under the MA gauge and first numerical results for the theory without abelian monopoles. The results support the idea that nonperturbative interaction arises between monopoles and residual abelian field and the other interactions are perturbative. It is shown that the Gribov region for the theory with the MA gauge fixed is non-connected.
We discuss a new approach to strong coupling expansion and dual representations for non-abelian lattice gauge theories. The Wilson gauge action is decomposed into a sum over "abelian color cycles" (ACC), which are loops around plaquettes visiting different colors at the corners. ACCs are complex numbers and thus commute such that a dual representation of a non-abelian theory can be obtained as in the abelian case. We apply the ACC approach to SU(2) and SU(3) lattice gauge theory and exactly rewrite the two partition sums in a strong coupling series where all gauge integrals are known in closed…
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