In this paper we improve the existing order parameter for monopole condensation in gauge theory vacuum, making it gauge-invariant from scratch and free of the spurious infrared problems which plagued the old one. Computing the new parameter on the lattice will unambiguously detect weather dual superconductivity is the mechanism for color confinement.
As a byproduct we relate confinement to the existence of a finite correlation length in the gauge-invariant correlator of chromo-electric field strengths.
It is proven that dual superconductivity of QCD vacuum in the confining phase is an intinsic property, independent on the choice of the abelian projection used to define the monopoles.
We investigate the connection between Color Confinement and thermal Abelian monopoles populating the deconfined phase of SU(2) Yang-Mills theory, by studying how the statistical properties of the monopole ensemble change as the confinement/deconfinement temperature is approached from above. In particular we study the distribution of monopole currents with multiple wrappings in the Euclidean time direction, corresponding to two or more particle permutations, and show that multiple wrappings increase as the deconfinement temperature is approached from above, in a way compatible with a condensati…
The condensation of monopoles (dual superconductivity) of QCD vacuum is reviewed. Direct evidence is produced that the system, in the confined phase, is a dual superconductor.
Monopole and photon contributions to Wilson loops are calculated using Monte-Carlo simulations of SU(2) QCD in the maximally abelian gauge. The string tensions of SU(2) QCD are well reproduced by extended monopole contributions alone.
An effective monopole action is derived from vacuum configurations after abelian projection in the maximally abelian gauge in $SU(2)$ QCD. Entropy dominance over energy of monopole loops is seen on the renormalized lattice with the spacing $b>b_c\simeq 5.2\times10^{-3} Λ_L^{-1}$ when the physical volume of the system is large enough. QCD confinement may be interpreted as the (dual) Meissner effect due to the monopole condensation.
We compare two competing conjectures of the color confinement in QCD, the monopole condensation and the Abelian dominance, and show that it is the monopole condensation which is responsible for the confinement. To demonstrate this we present a new gauge invariant integral expression of the one-loop QCD effective action which has no infra-red divergence. With this we show that, just as the GSO-projection restores the supersymmetry and modular invariance in NSR string theory, the color reflection invariance ("the C-projection") assures the gauge invariance and the stability of the monopole conde…
Thermal monopoles, identified after Abelian projection as magnetic currents wrapping non-trivially around the thermal circle, are studied in $N_f = 2+1$ QCD at the physical point. The distribution in the number of wrappings, which in pure gauge theories points to a condensation temperature coinciding with deconfinement, points in this case to around 275 MeV, almost twice the QCD crossover temperature $T_c$; similar indications emerge looking for the formation of a percolating current cluster. The possible relation with other non-perturbative phenomena observed above $T_c$ is discussed.
The disorder parameter $<μ>$ for the condensation of monopoles in QCD is estimated analytically in terms of gauge invariant field strength correlators. The continuum limit is discussed.
The evidence is reviewed for the mechanism of colour confinement in QCD by dual superconductivity of the ground state, i.e. by condensation of monopoles.
We investigate the recent conjecture that the chiral phase transition in non-compact lattice QED is driven by monopole condensation. The comparison of analytic and numerical results shows that we have a quantitative understanding of monopoles in both the quenched and dynamical cases. We can rule out monopole condensation.
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 discuss dynamics of N=2 supersymmetric SU(n_c) gauge theories with n_f quark hypermultiplets. Upon N=1 perturbation of introducing a finite mass for the adjoint chiral multiplet, we show that the flavor U(n_f) symmetry is dynamically broken to U(r) \times U(n_f-r), where r\leq [n_f/2] is an integer. This flavor symmetry breaking occurs due to the condensates of magnetic degrees of freedom which acquire flavor quantum numbers due to the quark zero modes. We briefly comment on the USp(2n_c) gauge theories. This talk is based on works with Giuseppe Carlino and Ken Konishi, hep-th/0001036 and h…
We investigate the dynamics of lattice gauge theories in an Abelian monopole background field. By means of the gauge-invariant lattice Schrodinger functional we study the Abelian monopole condensation in U(1) lattice gauge theory at zero temperature and in SU(3) lattice gauge theory at finite temperature.
We show that the QCD vacuum (without dynamical quarks) is a dual superconductor at least in the low-energy region in the sense that monopole condensation does really occur. In fact, we derive the dual Ginzburg-Landau theory (i.e., dual Abelian Higgs model) directly from the SU(2) Yang-Mills theory by adopting the maximal Abelian gauge. The dual superconductor can be on the border between type II and type I, excluding the London limit. The masses of the dual Abelian gauge field is expressed by the Yang-Mills gauge coupling constant and the mass of the off-diagonal gluon of the original Yang-Mil…
We use a lattice thermal partition functional to study Abelian monopole condensation in full QCD with $N_f=2$ staggered fermions. We present preliminary results on $16^3\times4$ and $32^3\times4$ lattices.
Recent studies of confinement based on the idea of abelian monopole condensation are reviewed briefly. Emphasis is placed on the approach to get the effective monoole action using the blockspin transformation on the dual lattice. The trajectory obtained looks to be the renormalized one in $SU(2)$ QCD. A disorder parameter of confinement is constructed. Monopole condensation occurs also in $SU(3)$ QCD.
We study the three dimensional Georgi-Glashow model (which interpolates smoothly between pure U(1) and SU(2) limits) using a constrained cooling which preserves 't Hooft-Polyakov monopoles. We find that the monopole-antimonopole condensation gives an area law for the Wilson loops. The monopole contribution to the string tension is close to the Monte Carlo value in the intermediate region.
New evidence is discussed of monopole condensation in the vacuum of SU(2) and SU(3) gauge theories. Monopoles defined by different abelian projections do condense in the transition to the confined phase and show the same behavior. For SU(2) critical indices are determined by finite size scaling analysis and the results agree with the 3d Ising Model, as expected.
Effective monopole actions for various extended monopoles are derived from vacuum configurations after abelian projection in the maximally abelian gauge in $T=0$ and $T\ne 0$ $SU(3)$ lattice QCD. The actions obtained appear to be independent of the lattice volume adopted. At zero temperature, monopole condensation is seen to occur from energy-entropy balance in the strong coupling region. Larger $β$ is included in the monopole condensed phase as more extended monopoles are considered. The scaling seen in the $SU(2)$ case is not yet observed. The renormalization flow diagram suggests the existe…
An effective monopole action for various extended monopoles is derived from vacuum configurations after abelian projection in the maximally abelian gauge in $SU(2)$ QCD. The action appears to be independent of the lattice volume. Moreover it seems to depend only on the physical lattice spacing of the renormalized lattice, not on $β$. Entropy dominance over energy of monopole loops is seen on the renormalized lattice with the spacing $b>b_c\simeq 5.2\times10^{-3} Λ_L^{-1}$. This suggests that monopole condensation always (for all $β$) occurs in the infinite-volume limit of lattice QCD.
We study the relation between the abelian monopole condensation and the deconfinement phase transition of the finite-temperature pure QCD. The expectation value of the monopole contribution to the Polyakov loop becomes zero when a long monopole loop is distributed uniformly in the configuration of the confinement phase. On the other hand, it becomes non-zero when the long monopole loop disappears in the deconfinement phase. We also discuss the relation between the monopole behaviors and the usual interpretation of the spontaneous breaking of Z(N) symmetry in finite-temperature SU(N) QCD. It is…
We study the continuum limit of adjoint SU(2) LGT by means of a suppression term for Z2 monopoles. High barriers for tunnelling among different twist sectors are overcome through parallel tempering. Monopole condensation is used to study the deconfinement transition and the properties of the confined phase. Ergodicity in summing over all twist sectors allows an unbiased measure of the 't Hooft vortices free energy. Its behaviour in the SO(3) confined phase hints at differences from what conjectured for semi-integer discretizations.
Two distinct phase transitions occur at different temperatures in QCD with adjoint fermions (aQCD): deconfinement and chiral symmetry restoration. In this model, quarks do no explicitely break the center Z(3) symmetry and therefore the Polyakov loop is a good order parameter for the deconfinement transition. We study monopole condensation by inspecting the expectation value of an operator which creates a monopole. Such a quantity is expected to be an order parameter for the deconfinement transition as in the case of fundamental fermions.
The confinement mechanism in the nonperturbative QCD is studied in terms of topological excitation as QCD-monopoles and instantons. In the 't Hooft abelian gauge, QCD is reduced into an abelian gauge theory with monopoles, and the QCD vacuum can be regarded as the dual superconductor with monopole condensation, which leads to the dual Higgs mechanism. The monopole-current theory extracted from QCD is found to have essential features of confinement. We find also close relation between monopoles and instantons using the lattice QCD. In this framework, the lowest $0^{++}$ glueball (1.5 $\sim$ 1.7…
It is offered to consider monopoles in Abelian Projection as quantum excitations which are solutions of the quantized Yang-Mills equations. According to the Heisenberg quantization method these equations are equivalent an infinite set of equations for Green's functions. A procedure for cutting off these infinite series of differential equations after some assumptions is offered. The received equations are identical to equations describing a dyon.
We investigate the Abelian monopole condensation in finite temperature SU(2) and SU(3) pure lattice gauge theories. To this end we introduce a gauge invariant disorder parameter built up in terms of the lattice Schrödinger functional. Our numerical results show that the disorder parameter is different from zero and Abelian monopole condense in the confined phase. On the other hand our numerical data suggest that the disorder parameter tends to zero, in the thermodynamic limit, when the gauge coupling constant approaches the critical deconfinement value. In the case of SU(3) we also compare the…
This is the short review of Monte-Carlo studies of quark confinement in lattice QCD. After abelian projections both in the maximally abelian and Polyakov gauges, it is seen that the monopole part alone is responsible for confinement. A block spin transformation on the dual lattice suggests that lattice $SU(2)$ QCD is always ( for all $β$) in the monopole condensed phase and so in the confinement phase in the infinite volume limit.
We demonstrate that the disorder parameter $<μ>$ to detect dual superconductivity in the confining phase of QCD is the v.e.v. of a magnetically charged, Dirac like, gauge invariant operator $μ$. We also show that the abelian projection on the lattice is determined up to terms O(a^2) (a = lattice spacing).
Finite size scaling studies of monopole condensation in noncompact quenched lattice $QED$ indicate an authentic second order phase transition lying in the universality class of four dimensional percolation. Since the upper critical dimension of percolation is six, the measured critical indices are far from mean-field values. We propose a simple set of ratios as the exact critical indices for this transition. The implication of these results for critical points in Abelian gauge theories are discussed.
Using the SU(2) lattice QCD, we formulate the dual Wilson loop and study the dual Higgs mechanism induced by monopole condensation in the maximally abelian (MA) gauge, where QCD is reduced into an abelian gauge theory including the electric current $j_μ$ and the monopole current $k_μ$. After the abelian projection in the MA gauge, the system can be separated into the photon part and the monopole part corresponding to the separation of $j_μ$ and $k_μ$, respectively. We study here the monopole part (the monopole-current system), which is responsible to the electric confinement. Owing to the abse…
Aspects of the monopole condensation picture of confinement are discussed. First, the nature of the monopole singularities in the abelian projection approach is analysed. Their apparent gauge dependence is shown to have a natural interpretation in terms of 't~Hooft-Polyakov-like monopoles in euclidean SU(2) gauge theory. Next, the results and predictions of a realization of confinement through condensation of such monopoles are summarized and compared with numerical data.
QCD with fermions in the adjoint representation (aQCD) is a model for which a deconfinement and a chiral phase transition take place at different temperatures. In this work, we present a study of the deconfinement transition in the dual superconductor picture based on the evaluation of an operator which carries magnetic charge. The expectation value of this operator signals monopole condensation and is an order parameter for deconfinement as in the case of fermions in the fundamental representation. We find a sharp first order deconfinement transition. We also study the effects of the chiral t…
In QCD with adjoint fermions (aQCD) the deconfining transition takes place at a lower temperature than the chiral transition. We study the two transitions by use of the Polyakov Loop, the monopole order parameter and the chiral condensate. The deconfining transition is first order, the chiral is a crossover. The order parameters for confinement are not affected by the chiral transition. We conclude that the degrees of freedom relevant to confinement are different from those describing chiral symmetry.
The deconfinement transition is studied close to the continuum limit of SO(3) lattice gauge theory. High barriers for tunnelling among different twist sectors causing loss of ergodicity for local update algorithms are circumvented by means of parallel tempering. We compute monopole and center vortex free energies both within the confining phase and through the deconfinement transition. We discuss in detail the general problem of defining order parameters for adjoint actions.
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 superconduc…
Color confinement can be understood by the dual Higgs theory, where monopole condensation leads to the exclusion of the electric flux from the QCD vacuum. We study the role of the monopole for color confinement by investigating the monopole current system. When the self-energy of the monopole current is small enough, long and complicated monopole world-lines appear, which is a signal of monopole condensation. In the dense monopole system, the Wilson loop obeys the area-law, and the string tension and the monopole density have similar behavior as the function of the self-energy, which seems tha…
The hypothesis is analysed that the monopoles condensing in QCD vacuum to make it a dual superconductor are classical solutions of the equations of motion.
The existence of the monopole condensation transition reported by Kocic et al. in non-compact, quenched QED is tested. No phase transition is found. This shows that divergence of the `monopole susceptibility' introduced by Hands and Wensley is not a reliable indicator of second order phase transitions. In view of these results I discuss claims that the chiral phase transition seen in QED with fermions is a lattice artefact driven by monopole condensation.
In recent work, we derived the long-distance confining dynamics of certain QCD-like gauge theories formulated on small $S^1 \times \R^3$ based on symmetries, an index theorem, and Abelian duality. Here, we give the microscopic derivation. The solution reveals a new mechanism of confinement in QCD(adj) in the regime where we have control over both perturbative and nonperturbative aspects. In particular, consider SU(2) QCD(adj) theory with $1 \leq n_f \leq 4$ Majorana fermions, a theory which undergoes gauge symmetry breaking at small $S^1$. If the magnetic charge of the BPS monopole is normaliz…
A direct connection is proved between the Non-Abelian Bianchi Identities and the Abelian Bianchi identities for the 't Hooft tensor in a generic gauge; the existence of a magnetic current is related to the violation of NABI's. Using this relation it is shown that not all gauges are equivalent to detect monopoles on the lattice, that e.g. the Maximal Abelian Gauge is a legitimate choice while the Landau gauge is not. Nevertheless monopole condensation is found to be a gauge invariant property.
It is shown that the creation of a monopole is a gauge invariant statement, based on topology. Creating a monopole is independent on the abelian projection in which it is created. This is fundamental in defining an order parameter for detecting dual superconductivity of the QCD vacuum.
We study the dual Higgs mechanism induced by monopole condensation based on the dual gauge formalism in the maximally abelian (MA) gauge in the lattice QCD. To examine ``monopole condensation'' in QCD, we study the monopole part or the monopole-current system appearing in the MA gauge by extracting the dual gluon field $B_μ$. First, we investigate the inter-monopole potential using the dual Wilson loop in the lattice QCD simulation. In the monopole part in the MA gauge, the inter-monopole potential is found to be flat, and can be fitted as the Yukawa potential in the infrared region. From more…
We discuss and propose a proper extension of the Abelian projection based on the Maximal Abelian Gauge to SU(N) gauge theories. Based, on that, we investigate the properties of thermal Abelian monopoles in the deconfined phase of the SU(3) pure gauge theory. Such properties are very similar to those already found for SU(2), confirming the relevance of the magnetic component close to Tc and the possible condensation of thermal monopoles as the deconfinement temperature is crossed from above. Moreover, we study the correlation functions among monopoles related to different U(1) subgroups, which …
We study the confinement physics in QCD in the maximally abelian (MA) gauge using the SU(2) lattice QCD, based on the dual-superconductor picture. In the MA gauge, off-diagonal gluon components are forced to be small, and the off-diagonal angle variable $χ_μ(s)$ tends to be random. Within the random-variable approximation for $χ_μ(s)$, we analytically prove the perimeter law of the off-diagonal gluon contribution to the Wilson loop in the MA gauge, which leads to abelian dominance on the string tension. To clarify the origin of abelian dominance for the long-range physics, we study the charged…
Classical solutions corresponding to monopole-antimonopole pairs are found in 3d and 4d SU(2) and U(1) lattice gauge theories. The stability of these solutions in different theories is studied.
We generate a random instanton vacuum with various densities and size distributions. We perform numerically the maximally abelian gauge fixing of these configurations in order to find monopole trajectories induced by instantons. We find that instanton-induced monopole loops form enormous clusters occupying the whole physical volume, provided instantons are sufficiently dense. It indicates that confinement might be caused by instantons.
It is possible to derive a monopole action from vacuum configurations obtained in Monte-Carlo simulations extending the method developed by Swendsen. We apply the method to compact QED both in the Villain and in the Wilson forms. The action of the natural monopoles in the Villain case is in fairly good agreement with that derived by the exact dual transformation. Comparing the monopole actions, we find (1) the DeGrand-Toussaint monopole definition may be useful for $β_V $ larger than about 0.5, (2) the Villain model well approximates the Wilson one for $β$ smaller than $β_c$ and (3) in the Wil…
We study the confinement physics in QCD in the maximally abelian (MA) gauge using the SU(2) lattice QCD. To clarify the origin of abelian dominance for the long-range physics, we study the charged-gluon propagator in the lattice QCD, and find that the effective mass $m_{ch} \simeq 0.9 {\rm GeV}$ of the charged gluon is induced by the MA gauge fixing. In the MA gauge, there appears the global network of the monopole world-line covering the whole system, which would be identified as monopole condensation at a large scale. To prove monopole condensation, we apply the dual gauge formalism to the m…
We study the relation between instantons and monopoles in the abelian gauge. First, we investigate the monopole in the multi-instanton solution in the continuum Yang-Mills theory using the Polyakov gauge. At a large instanton density, the monopole trajectory becomes highly complicated, which can be regarded as a signal of monopole condensation. Second, we study instantons and monopoles in the SU(2) lattice gauge theory both in the maximally abelian (MA) gauge and in the Polyakov gauge. Using the $16^3 \times 4$ lattice, we find monopole dominance for instantons in the confinement phase even at…
We aim to show the effects of the magnetic monopoles and instantons in quantum chromodynamics (QCD) on observables; therefore, we introduce a monopole and anti-monopole pair in the QCD vacuum of a quenched SU(3) by applying the monopole creation operator to the vacuum. We calculate the eigenvalues and eigenvectors of the overlap Dirac operator that preserves the exact chiral symmetry in lattice gauge theory using these QCD vacua. We then investigate the effects of magnetic monopoles and instantons. First, we confirm the monopole effects as follows: (i) The monopole creation operator makes the …
We study, by means of numerical lattice simulations, the properties of the reconfinement phase transition taking place in trace deformed $SU(3)$ Yang-Mills theory defined on $\mathbb{R}^3\times S^1$, in which center symmetry is recovered even for small compactification radii. We show, by means of a finite size scaling analysis, that the reconfinement phase transition is first-order, like the usual $SU(3)$ thermal phase transition. We then investigate two different physical phenomena, which are known to characterize the standard confinement/deconfinement phase transition, namely the condensatio…
We study the QCD vacuum structure under the influence of an electromagnetic field with a nonzero second Lorentz invariant $I_2=\vec{E}\cdot{\vec B}$. We show that the presence of $I_2$ can induce neutral pion ($π^0$) condensation in the QCD vacuum through the electromagnetic triangle anomaly. Within the frameworks of chiral perturbation theory at leading small-momenta expansion as well as the Nambu--Jona-Lasinio model at leading $1/N_c$ expansion, we quantify the dependence of the $π^0$ condensate on $I_2$. The stability of the $π^0$-condensed vacuum against the Schwinger charged pair producti…
We investigate the confining properties of the QCD vacuum with $N_f=2$ flavors of dynamical quarks, and compare the results with the properties of the quenched theory. We use non-perturbatively $\mathcal{O}(a)$ improved Wilson fermions to keep cut-off effects small. We focus on color magnetic monopoles. Among the quantities we study are the monopole density and the monopole screening length, the static potential and the profile of the color electric flux tube. We furthermore derive the low-energy effective monopole action. Marked differences between the quenched and dynamical vacuum are found.
The order parameter for monopole condensation is computed in terms of gauge invariant field strength correlators. Important properties emerge of the correlators in the confined phase, which could not be extracted by existing numerical determinations on the lattice.
We propose to use the different kinds of vacua of the gauge theories coupled to matter as a laboratory to test confinement ideas of pure Yang-Mills theories. In particular, the very poor overlap of the Wilson loop with the broken string states supports the 't Hooft and Mandelstam confinement criteria. However in the Z(2) gauge-Higgs model we use as a guide we find that the condensation of monopoles and center vortices is a necessary, but not sufficient condition for confinement.
Monopole Percolation was first introduced in the study of the non-compact lattice QED in both, the pure case and coupled to Higgs fields. Monopole percolation has been also observed coupled to the monopole condensation in the study of the pure gauge compact QED. We present here the results coming from the analysis of the role of the monopole percolation in the coupled gauge-higgs compact QED.
