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Register a new userClear correlation between monopoles and the chiral condensate in SU(3) QCD
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Hiroki Ohata
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We study spontaneous chiral-symmetry breaking in SU(3) QCD in terms of the dual superconductor picture for quark confinement in the maximally Abelian (MA) gauge, using lattice QCD Monte Carlo simulations with four different lattices of $16^4$, $24^4$, $24^3times 6$ at $beta=6.0$ (i.e., the spacing $a simeq$ 0.1 fm), and $32^4$ at $beta=6.2$ (i.e., $a simeq$ 0.075 fm), at the quenched level. First, in the confinement phase, we find Abelian dominance and monopole dominance in the MA gauge for the chiral condensate in the chiral limit,using the two different methods of i) the Banks-Casher relation with the Dirac eigenvalue density and ii) finite quark-mass calculations with the quark propagator and its chiral extrapolation. In the high-temperature deconfined phase, the chiral restoration is observed also for the Abelian and the monopole sectors. Second, we investigate local correlation between the chiral condensate and monopoles, which topologically appear in the MA gauge. We find that the chiral condensate locally takes a quite large value near monopoles. As an interesting possibility, the strong magnetic field around monopoles is responsible to chiral symmetry breaking in QCD, similarly to the magnetic catalysis.
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Using the lattice gauge field theory, we study the relation among the local chiral condensate, monopoles, and color magnetic fields in quantum chromodynamics (QCD). First, we investigate idealized Abelian gauge systems of 1) a static monopole-antimonopole pair and 2) a magnetic flux without monopoles, on a four-dimensional Euclidean lattice. In these systems, we calculate the local chiral condensate on quasi-massless fermions coupled to the Abelian gauge field, and find that the chiral condensate is localized in the vicinity of the magnetic field. Second, using SU(3) lattice QCD Monte Carlo calculations, we investigate Abelian projected QCD in the maximally Abelian gauge, and find clear correlation of distribution similarity among the local chiral condensate, monopoles, and color magnetic fields in the Abelianized gauge configuration. As a statistical indicator, we measure the correlation coefficient $r$, and find a strong positive correlation of $r simeq 0.8$ between the local chiral condensate and an Euclidean color-magnetic quantity ${cal F}$ in Abelian projected QCD. The correlation is also investigated for the deconfined phase in thermal QCD. As an interesting conjecture, like magnetic catalysis, the chiral condensate is locally enhanced by the strong color-magnetic field around the monopoles in QCD.
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.
We present the first study of the Abelian-projected gluonic-excitation energies for the static quark-antiquark (Q$bar{rm Q}$) system in SU(3) lattice QCD at the quenched level, using a $32^4$ lattice at $beta = 6.0$. We investigate ground-state and three excited-state Q$bar{rm Q}$ potentials, using smeared link variables on the lattice. We find universal Abelian dominance for the quark confinement force of the excited-state Q$bar{rm Q}$ potentials as well as the ground-state potential. Remarkably, in spite of the excitation phenomenon in QCD, we find Abelian dominance for the first gluonic-excitation energy of about 1 GeV at long distances in the maximally Abelian gauge. On the other hand, no Abelian dominance is observed for higher gluonic-excitation energies even at long distances. This suggests that there is some threshold between 1 and 2 GeV for the applicable excitation-energy region of Abelian dominance. Also, we find that Abelian projection significantly reduces the short-distance $1/r$-like behavior in gluonic-excitation energies.
To check the dual superconductor picture for the quark-confinement mechanism, we evaluate monopole dominance as well as Abelian dominance of quark confinement for both quark-antiquark and three-quark systems in SU(3) quenched lattice QCD in the maximally Abelian (MA) gauge. First, we examine Abelian dominance for the static $Qbar Q$ system in lattice QCD with various spacing $a$ at $beta$=5.8-6.4 and various size $L^3$x$L_t$. For large physical-volume lattices with $La ge$ 2fm, we find perfect Abelian dominance of the string tension for the $Qbar Q$ systems: $sigma_{Abel} simeq sigma$. Second, we accurately measure the static 3Q potential for more than 300 different patterns of 3Q systems with 1000-2000 gauge configurations using two large physical-volume lattices: ($beta$,$L^3$x$L_t$)=(5.8,$16^3$x32) and (6.0,$20^3$x32). For all the distances, the static 3Q potential is found to be well described by the Y-Ansatz: two-body Coulomb term plus three-body Y-type linear term $sigma L_{min}$, where $L_{min}$ is the minimum flux-tube length connecting the three quarks. We find perfect Abelian dominance of the string tension also for the 3Q systems: $sigma^{Abel}_{3Q}simeq sigma_{3Q} simeq sigma$. Finally, we accurately investigate monopole dominance in SU(3) lattice QCD at $beta$=5.8 on $16^3$x32 with 2,000 gauge configurations. Abelian-projected QCD in the MA gauge has not only the color-electric current $j^mu$ but also the color-magnetic monopole current $k^mu$, which topologically appears. By the Hodge decomposition, the Abelian-projected QCD system can be divided into the monopole part ($k_mu e 0$, $j_mu=0$) and the photon part ($j_mu e 0$, $k_mu=0$). We find monopole dominance of the string tension for $Qbar Q$ and 3Q systems: $sigma_{Mo}simeq 0.92sigma$. While the photon part has almost no confining force, the monopole part almost keeps the confining force.
The long standing problem is solved why the number and the location of monopoles observed in Lattice configurations depend on the choice of the gauge used to detect them, in contrast to the obvious requirement that monopoles, as physical objects, must have a gauge-invariant status. It is proved, by use of non-abelian Bianchi identities, that monopoles are indeed gauge-invariant: the technique used to detect them has instead an efficiency which depends on the choice of the abelian projection, in a known and controllable way.
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