Dual Superconductor Research Articles

Gauge-invariant gluon mass, infrared Abelian dominance, and stability of magnetic vacuum

We give an argument for deriving analytically the infrared “Abelian” dominance in a gauge invariant way for the Wilson loop average in SU(2) Yang– Mills theory. In other words, we propose a possible mechanism for realizing the dynamical Abelian projection in the SU(2) gauge-invariant manner without breaking color symmetry. This supports validity of the dual superconductivity picture for quark confinement. We also discuss the stability of the vacuum with magnetic condensation as a by-product of this result.

Vortex duality: Observing the dual nature using order propagators

In condensed matter physics, Kramers-Wannier duality implies that the state disordered by quantum fluctuations or temperature actually corresponds to an ordered state formed from the topological excitations of the ``original'' ordered state. At first sight it might appear to be impossible to observe this dual order using means associated with the original order. Although true for Ising models, we demonstrate in this paper that this is not a general statement by considering the well-known vortex duality, in particular in the quantum interpretation in $2+1\mathrm{D}$ where it is associated with the quantum phase transition from a superfluid to a Bose Mott insulator. Here, the disordered Mott insulating state is at the same time a dual superconductor corresponding to a Bose condensate of vortices. We present a simple formalism making it possible to compute the velocity propagator associated with the superfluid in terms of the degrees of freedom of the dual theory. The Mott insulator is characterized by a doublet of massive modes, and we demonstrate that one of these modes is nothing else than the longitudinal photon (gauged second sound) of the dual superconductor. For increasing momenta, the system rediscovers the original order, and the effect on the velocity correlator is that the longitudinal photon loses its pole strength. The quantum critical regime as probed by the velocity correlator is most interesting. We demonstrate that at infinite wavelength the continua of critical modes associated with second sound and the dual longitudinal photon are indistinguishable. However, at finite momenta they behave differently, tracking the weight reshuffling found in the quasiparticle spectrum of the disorder state closely.

Light Nonabelian Monopoles: Constructing Dual Nonabelian Superconductor of More General Types

In this talk we discuss a new class of N = 1 supersymmetric U(N) gauge theories, in which the low-energy magnetic effective gauge group contains multiple nonabelian factors, Π i SU(r i ), supported by light monopoles carrying associated charges. These nontrivially generalize the physics of r-vacua found in softly broken N = 2 supersymmetric QCD and yield dual nonabelian superconductor of a more general type. The matching between classical and quantum (r 1 , r 2 ,...) vacua leads to nontrivial hints about the nonabelian duality.

Analytic Invariant Charge in QCD with Suppression of Nonperturbative Contributions at Large Q 2

Based on the analytic invariant charge obtained from the results of the standard perturbation theory up to the four-loop approximation, we construct a “synthetic” model of the invariant charge in quantum chromodynamics. In the suggested model, the perturbative discontinuity on the timelike semiaxis in the complex Q2 plane is preserved, and nonperturbative contributions not only cancel nonphysical perturbation theory singularities in the infrared region but also rapidly decrease in the ultraviolet region. On one hand, the effective coupling function in this model is enhanced at zero (the dual superconductivity property of the quantum chromodynamics vacuum); on the other hand, a dynamical gluon mass appears. In our approach, fixing the parameter corresponding to the string tension parameter and normalizing (for example, at the point Mτ) entirely fix the synthetic invariant-charge model. The dynamical gluon mass mg is then fixed and is stable as the number of loops of the original perturbative approximation increases.

Vacuum type of SU(2) gluodynamics in maximally Abelian and Landau gauges

The vacuum type of SU(2) gluodynamics is studied using Monte-Carlo simulations in maximally Abelian (MA) gauge and in Landau (LA) gauge, where the dual Meissner effect is observed to work. The dual Meissner effect is characterized by the coherence and the penetration lengths. Correlations between Wilson loops and electric fields are evaluated in order to measure the penetration length in both gauges. The coherence length is shown to be fixed in the MA gauge from measurements of the monopole density around the static quark-antiquark pair. It is also shown numerically that a dimension 2 gluon operator A^+A^-(s) and the monopole density has a strong correlation as suggested theoretically. Such a correlation is observed also between the monopole density and A^2(s)= A^+A^-(s) + A^3A^3(s) condensate if the remaining U(1) gauge degree of freedom is fixed to U(1) Landau gauge (U1LA). The coherence length is determined numerically also from correlations between Wilson loops and A^+A^-(s) and A^2(s) in MA + U1LA gauge. Assuming that the same physics works in the LA gauge, we determine the coherence length from correlations between Wilson loops and A^2(s). Penetration lengths and coherence lengths in the two gauges are almost the same. The vacuum type of the confinement phase in both gauges is near to the border between the type 1 and the type 2 dual superconductors.

Mixed heavy-quark–gluon condensate in the stochastic vacuum model and dual superconductor

The world-line formalism is used for the evaluation of the mixed heavy-quark-gluon condensate in two models of QCD - the stochastic vacuum model and the dual superconductor one. Calculations are performed for an arbitrary dimensionality of space-time $d\ge 2$. While in the stochastic vacuum model, the condensate is UV finite up to $d=8$, in the dual superconductor model it is UV divergent at any $d\ge 2$. A regularization of this divergence is proposed, which makes quantitative the condition of the type-II dual superconductor. The obtained results are generalized to the case of finite temperatures. Corrections to the both, mixed and standard, heavy-quark condensates, which appear due to the variation of the gauge field at the scale of the vacuum correlation length, are evaluated within the stochastic vacuum model. These corrections diminish the absolute values of the condensates, as well as the ratio of the mixed condensate to the standard one.

Magnetic condensation, Abelian dominance, and instability of Savvidy vacuum in Yang-Mills theory

We propose a novel type of color magnetic condensation originating from magnetic monopoles so that it provides the mass of off-diagonal gluons in the Yang-Mills theory. This dynamical mass generation enables us to explain the infrared Abelian dominance and monopole dominance by way of a non-Abelian Stokes theorem, which supports the dual superconductivity picture of quark confinement. Moreover, we show that the instability of Savvidy vacuum disappears by sufficiently large color magnetic condensation.

Model of phase fluctuations in a latticed-wave superconductor: Application to the Cooper-pair charge-density wave in underdoped cuprates

We introduce and study an $XY$-type model of thermal and quantum phase fluctuations in a two-dimensional correlated lattice $d$-wave superconductor based on the ${\mathrm{QED}}_{3}$ effective theory of high-temperature superconductors. General features of and selected results obtained within this model were reported earlier in an abbreviated format (Z. Te\ifmmode \check{s}\else \v{s}\fi{}anovi\ifmmode \acute{c}\else \'{c}\fi{}, e-print cond-mat/0405235). The model is geared toward describing not only the long distance but also the intermediate length-scale physics of underdoped cuprates. In particular, we elucidate the dynamical origin and investigate specific features of the charge-density wave of Cooper pairs, which we argue is the state behind the periodic charge-density modulation discovered in recent scanning-tunneling-microscopy experiments. We illustrate how Mott-Hubbard correlations near half-filling suppress superfluid density and favor an incompressible state which breaks translational symmetry of the underlying atomic lattice. We show how the formation of the Cooper pair charge-density wave in such a strongly quantum fluctuating superconductor can naturally be understood as an Abrikosov-Hofstadter problem in a type-II dual superconductor, with the role of the dual magnetic field played by the electron density. The resulting Abrikosov lattice of dual vortices translates into a periodic modulation of the Bogoliubov--de Gennes (BdG) gap function and the electronic density. We numerically study the energetics of various Abrikosov-Hofstadter dual vortex arrays and compute their detailed signatures in the single-particle local tunneling density of states. A $4\ifmmode\times\else\texttimes\fi{}4$ checkerboard-type modulation pattern naturally arises as an energetically favored ground state at and near the $x=1∕8$ doping and produces the local density of states in good agreement with experimental observations. The leading-order behavior of nodal BdG fermions remains unaffected.

Color confinement and dual superconductivity of the vacuum. IV

Color confinement and dual superconductivity of the vacuum. IV

A numerical study of confinement in compact QED

Compact U(1) lattice gauge theory in four dimensions is studied by means of an efficient algorithm which exploits the duality transformation properties of the model. We focus our attention onto the confining regime, considering the interquark potential and force, and the electric field induced by two infinitely heavy sources. We consider both the zero and finite temperature setting, and compare the theoretical predictions derived from the effective string model and the dual superconductor scenario to the numerical results.

String breaking in QCD: dual superconductor vs. stochastic vacuum model

Effects of dispersion of the chromoelectric field of the flux tube on the string-breaking distance are studied. The leading-order correction is shown to slightly diminish the result following from the Schwinger formula. Instead, accounting for corrections of all orders might result, at certain values of the Landau-Ginzburg parameter, in an increase of the string-breaking distance up to one order of magnitude. An alternative formula for this distance is obtained when produced pairs are treated as holes in a confining pellicle, which spans over the contour of an external quark-antiquark pair. Generalizations of the obtained results to the cases of small temperatures, as well as temperatures close to the critical one are also discussed.

Chiral symmetry breaking and monopole condensation in QCD

We show that, in the dual superconductor picture of the QCD vacuum, the presence of the monopole condensate inevitably leads to the breaking of the chiral symmetry.

Charge Modulation, Spin Response, and Dual Hofstadter Butterfly in High-TcCuprates

The modulated density of states observed in recent STM experiments in underdoped cuprates is argued to be a manifestation of the charge-density wave of Cooper pairs (CPCDW). CPCDW formation is due to superconducting phase fluctuations enhanced by Mott-Hubbard correlations near half-filling. The physics behind the CPCDW is related to a Hofstadter problem in a dual superconductor. It is shown that CPCDW does not impact nodal fermions at the leading order. An experiment is proposed to probe coupling of the CPCDW to the spin carried by nodal quasiparticles.

Topological aspects of dual superconductors

We discuss topological aspects of two-gap superconductors with and without Josephson coupling between gaps. We address nontrivial topological aspects of the dual superconductors and its connections to Meissner effect and flux quantization. The topological knotted string geometry is also discussed in terms of the Hopf invariant, curvature and torsion of the strings associated with U(1)$\times$U(1) gauge group.

Baryonic flux in quenched and two-flavor dynamical QCD after Abelian projection

We study the distribution of color electric flux of the three-quark system in quenched and full QCD (with N_f = 2 flavors of dynamical quarks) at zero and finite temperature. To reduce ultra-violet fluctuations, the calculations are done in the abelian projected theory fixed to the maximally abelian gauge. In the confined phase we find clear evidence for a Y--shape flux tube surrounded and formed by the solenoidal monopole current, in accordance with the dual superconductor picture of confinement. In the deconfined, high temperature phase monopoles cease to condense, and the distribution of the color electric field becomes Coulomb--like.

Magnetic condensation, Abelian dominance, and instability of Savvidy vacuum

We show that a certain type of color magnetic condensation originating from magnetic monopole configurations is sufficient to provide the mass for off-diagonal gluons in the SU ( 2 ) Yang–Mills theory under the Cho–Faddeev–Niemi decomposition. We point out that the generated gluon mass can cure the instability of the Savvidy vacuum. In fact, such a novel type of magnetic condensation is shown to occur by calculating the effective potential. This enables us to explain the infrared Abelian dominance and monopole dominance by way of a non-Abelian Stokes theorem, which suggests the dual superconductivity picture of quark confinement. Finally, we discuss the implication to the Faddeev–Skyrme model with knot soliton as a low-energy effective theory of Yang–Mills theory.

A finite temperature investigation of dual superconductivity in the modified [formula omitted] lattice gauge theory

We study the SO(3) lattice gauge theory in 3+1 dimensions with the adjoint Wilson action modified by a Z2 monopole suppression term and by means of the Pisa disorder operator. We find evidence for a finite temperature deconfinement transition driven by the condensation of U(1) magnetic charges. A finite-size scaling test shows consistency with the critical exponents of the 3D Ising model.

Dual Superconductors And Su(2) Yang-Mills

We propose that the SU(2) Yang-Mills theory can be interpreted as a two-band dual superconductor with an interband Josephson coupling. We discuss various consequences of this interpretation including electric flux quantization, confinement of vortices with fractional flux, and the possibility that a closed vortex loop exhibits exotic exchange statistics.

Determination of the monopole condensate from monopole action in quenched SU(2) QCD

We study the effective monopole action obtained in the maximal Abelian projection of the quenched SU(2) lattice QCD. We determine the quadratic part of the lattice action using analytical blocking from the continuum dual superconductor model to the lattice model. The leading contribution to the quadratic action depends explicitly on the value of the monopole condensate. We show that the analytical monopole action matches the numerically obtained action in quenched SU(2) QCD with a good accuracy. The comparison of numerical and analytical results gives us the value of the monopole condensate in quenched SU(2) QCD, $\ensuremath{\eta}=243(42)\mathrm{MeV}.$

Monopoles in the Abelian Polyakov gauge and projection (in)dependence of the dual superconductor mechanism of confinement

We discuss the effect of the choice of an Abelian projection on the dual superconductor mechanism of confinement in SU(2) gluodynamics. Using qualitative arguments we show that the dual superconductor Lagrangian corresponding to the Abelian Polyakov gauge has a different structure compared to the dual Lagrangian in the Maximal Abelian gauge. A difference between these Lagrangians reflects the fact that in continuum limit the monopoles should be static in the Abelian Polyakov gauge and therefore these monopoles can not give rise to the confinement of static quarks. Using the Abelian Polyakov gauge as an example, we show that (i) the dual superconductor scenario of confinement may depend on the Abelian projection; (ii) the condensation of the Abelian monopoles - which may be realized in any Abelian projection - is necessary but not sufficient condition for confinement. These results do not exclude an existence of a class of Abelian gauges in which the dual superconductor scenario works well.