Seikou Kato

Perfect monopole action for infrared SU(2) QCD

Abstract Performing block-spin transformations on the dual lattice after abelian projection, we obtain an almost perfect lattice action in terms of monopole currents in the infrared region of pure SU (2) QCD. The action depends only on a physical scale b and is free from a cut-off a ( β ). It reproduces analytically the string tension which is near the physical one for a wide physical-scale region (b ⩾ 1.0(κ −1 2 )) .

Lattice construction of Cho-Faddeev-Niemi decomposition and gauge invariant monopole

Abstract We present the first implementation of the Cho–Faddeev–Niemi decomposition of the SU(2) Yang–Mills field on a lattice. Our construction retains the color symmetry (global SU(2) gauge invariance) even after a new type of maximally Abelian gauge, as explicitly demonstrated by numerical simulations. Moreover, we propose a gauge-invariant definition of the magnetic monopole current using this formulation and compare the new definition with the conventional one by DeGrand and Toussaint to exhibit its validity.

Compact lattice formulation of Cho–Faddeev–Niemi decomposition: Gluon mass generation and infrared Abelian dominance

Abstract This Letter complements a new lattice formulation of SU(2) Yang–Mills theory written in terms of new variables in a compact form proposed in the previous paper. The new variables used in the formulation were once called the Cho–Faddeev–Niemi or Cho–Faddeev–Niemi–Shabanov decomposition. Our formulation enables us to explain the infrared “Abelian” dominance, in addition to magnetic monopole dominance shown in the previous paper, in the gauge invariant way without relying on the specific gauge fixing called the maximal Abelian gauge used in the conventional investigations. In this Letter, especially, we demonstrate by numerical simulations that gluon degrees of freedom other than the “Abelian” part acquire the mass to be decoupled in the low-energy region leading to the infrared Abelian dominance.

Almost perfect quantum lattice action for low-energy SU(2) gluodynamics

We study various representations of infrared effective theory of SU(2) Gluodynamics as a (quantum) perfect lattice action. In particular we derive a monopole action and a string model of hadrons from SU(2) Gluodynamics. These are lattice actions which give almost cut-off independent physical quantities even on coarse lattices. The monopole action is determined by numerical simulations in the infrared region of SU(2) Gluodynamics. The string model of hadrons is derived from the monopole action by using BKT transformation. We illustrate the method and evaluate physical quantities such as the string tension and the mass of the lowest state of the glueball analytically using the string model of hadrons. It turns out that the classical results in the string model is near to the one in quantum SU(2) Gluodynamics. PACS: 12.38.Gc, 11.15.Ha

Non-Abelian dual superconductor picture for quark confinement

We give a theoretical framework for defining and extracting non-Abelian magnetic monopoles in a gauge-invariant way in SU(N) Yang-Mills theory to study quark confinement. Then we give numerical evidences that the non-Abelian magnetic monopole defined in this way gives a dominant contribution to confinement of fundamental quarks in SU(3) Yang-Mills theory, which is in sharp contrast to the SU(2) case in which Abelian magnetic monopoles play the dominant role for quark confinement.

New descriptions of lattice SU(N) Yang-Mills theory towards quark confinement

Abstract We give new descriptions of lattice SU ( N ) Yang–Mills theory in terms of new lattice variables. The validity of such descriptions has already been demonstrated in the SU ( 2 ) Yang–Mills theory by our previous works from the viewpoint of defining and extracting topological degrees of freedom such as gauge-invariant magnetic monopoles and vortices which play the dominant role in quark confinement. In particular, we have found that the SU ( 3 ) lattice Yang–Mills theory has two possible options, maximal and minimal: The existence of the minimal option has been overlooked so far, while the maximal option reproduces the conventional SU ( 3 ) Cho–Faddeev–Niemi–Shabanov decomposition in the naive continuum limit. The new description gives an important framework for understanding the mechanism of quark confinement based on the dual superconductivity.

Compact lattice formulation of Cho–Faddeev–Niemi decomposition: String tension from magnetic monopoles

Abstract In this Letter we begin on a new lattice formulation of the non-linear change of variables called the Cho–Faddeev–Niemi decomposition in SU ( 2 ) Yang–Mills theory. This is a compact lattice formulation improving the non-compact lattice formulation proposed in our previous paper. Based on this formulation, we propose a new gauge-invariant definition of the magnetic monopole current which guarantees the magnetic charge quantization and reproduces the conventional magnetic-current density obtained in the Abelian projection based on the DeGrand–Toussaint method. Finally, we demonstrate the magnetic monopole dominance in the string tension in SU ( 2 ) Yang–Mills theory on a lattice. Our formulation enables one to reproduce in the gauge-invariant way remarkable results obtained so far only in the maximally Abelian gauge.

A quantum perfect lattice action for monopoles and strings

A quantum perfect lattice action in four dimensions can be derived analytically as a renormalized trajectory when we perform a block spin transformation of monopole currents in a simple but non-trivial case of quadratic monopole interactions. The spectrum of the lattice theory is identical to that of the continuum theory. The perfect monopole action is transformed exactly into a lattice action of a string model. A perfect operator evaluating a static potential between electric charges is also derived explicitly. If the monopole interactions are weak as in the case of infrared SU(2) QCD, the string interactions become strong. The static potential and the string tension is estimated analytically by the use of the strong coupling expansion and the continuum rotational invariance is restored completely.Abstract A quantum perfect lattice action in four dimensions can be derived analytically as a renormalized trajectory when we perform a block spin transformation of monopole currents in a simple but non-trivial case of quadratic monopole interactions. The spectrum of the lattice theory is identical to that of the continuum theory. The perfect monopole action is transformed exactly into a lattice action of a string model. A perfect operator evaluating a static potential between electric charges is also derived explicitly. If the monopole interactions are weak as in the case of infrared SU (2) QCD, the string interactions become strong. The static potential and the string tension is estimated analytically by the use of the strong coupling expansion and the continuum rotational invariance is restored completely.

Non-Abelian dual superconductivity in SU(3) Yang-Mills theory: dual Meissner effect and type of the vacuum

We have proposed the non-Abelian dual superconductivity picture for quark confinement in the SU(3) Yang-Mills (YM) theory, and have given numerical evidences for the restricted-field dominance and the non-Abelian magnetic monopole dominance in the string tension by applying a new formulation of the YM theory on a lattice. To establish the non-Abelian dual superconductivity picture for quark confinement, we have observed the non-Abelian dual Meissner effect in the SU(3) Yang-Mills theory by measuring the chromoelectric flux created by the quark-antiquark source, and the non-Abelian magnetic monopole currents induced around the flux. We conclude that the dual superconductivity of the SU(3) Yang-Mills theory is strictly the type I and that this type of dual superconductivity is reproduced by the restricted field and the non-Abelian magnetic monopole part, in sharp contrast to the SU(2) case: the border of type I and type II.

Three topics of monopole dynamics in abelian projected QCD

Abstract Three topics about monopole dynamics after abelian projection are reported. The first is the new and detailed analyses of SU (2) monopole action obtained after the block-spin transformation on the dual lattice. The b = na (β) dependence for all couplings are well fitted with a universal curve. The distance dependence of the couplings is well reproduced by a massive propagator with the mass m = 0.8 in unit of b . The second is the SU (3) monopole action recently obtained. The third is new interesting gauges showing abelian and monopole dominances as in the maximally abelian gauge.