Quark confinement and gauge invariant monopoles in SU(2) YM (original) (raw)
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Proceedings of The XXVI International Symposium on Lattice Field Theory — PoS(LATTICE 2008), 2009
We propose a new description of the SU(N) Yang-Mills theory on a lattice, which enables one to explain quark confinement based on the dual superconductivity picture in a gauge independent way. This is because we can define gauge-invariant magnetic monopoles which are inherent in the Wilson loop operator. For SU(3) there are two options: the minimal option with a single type of non-Abelian magnetic monopole characterized by the maximal stability subgroupH = U(2) = SU(2) ×U(1), and the maximal one with two types of Abelian magnetic monopoles characterized by the maximal torus subgroupH = U(1) ×U(1). The maximal option corresponds to a gauge independent reformulation of the Abelian projection represented by the conventional MAG. In the minimal option, we have successfully performed the numerical simulation of the SU(3) Yang-Mills theory on a lattice. We give preliminary numerical results showing the dominance of the non-Abelian magnetic monopole in the string tension obtained from the Wilson loop in the fundamental representation, and the infrared dominance of a decomposed field variable for correlation functions after demonstrating the preservation of color symmetry which was explicitly broken by the conventional MAG.
A new description of lattice Yang-Mils theory and non-Abelian monopoles as the quark confiner
We propose a new description of the SU(N) Yang-Mills theory on a lattice, which enables one to explain quark confinement based on the dual superconductivity picture in a gauge independent way. This is because we can define gauge-invariant magnetic monopoles which are inherent in the Wilson loop operator. For SU(3) there are two options: the minimal option with a single type of non-Abelian magnetic monopole characterized by the maximal stability subgroupH = U(2) = SU(2) ×U(1), and the maximal one with two types of Abelian magnetic monopoles characterized by the maximal torus subgroupH = U(1) × U(1). The maximal option corresponds to a gauge independent reformulation of the Abelian projection represented by the conventional MAG. In the minimal option, we have successfully performed the numerical simulation of the SU(3) Yang-Mills theory on a lattice. We give preliminary numerical results showing the dominance of the non-Abelian magnetic monopole in the string tension obtained from the Wilson loop in the fundamental representation, and the infrared dominance of a decomposed field variable for correlation functions after demonstrating the preservation of color symmetry which was explicitly broken by the conventional MAG.
String tension from monopoles in SU(2) lattice gauge theory
Physical Review D, 1994
We calculate the heavy quark potential from the magnetic current due to monopoles in four dimensional SU(2) lattice gauge theory. The magnetic current is located in configurations generated in a conventional Wilson action simulation on a 16 4 lattice. The configurations are projected with high accuracy into the maximum abelian gauge. The magnetic current is then extracted and the monopole contribution to the potential is calculated. The resulting string tension is in excellent agreement with the SU(2) string tension obtained by conventional means from the configurations. Comparison is made with the U(1) case, with emphasis on the differing periodicity properties of SU(2) and U(1) lattice gauge theories. The properties of the maximum abelian gauge are discussed.
Magnetic monopoles in pure SU(2)SU (2)SU(2) Yang–Mills theory with a gauge-invariant mass
Progress of Theoretical and Experimental Physics, 2018
In this paper, we show the existence of magnetic monopoles in the pure SU (2) Yang-Mills theory when a gauge-invariant mass term is introduced. This result follows from the recent proposal for obtaining gauge field configurations in the Yang-Mills theory from the solutions of the field equations in the "complementary" gauge-scalar model. The gauge-invariant mass term is obtained through a change of variables and a gauge-independent description of the Brout-Englert-Higgs mechanism, which relies neither on the spontaneous breaking of gauge symmetry nor on the assumptions of the nonvanishing vacuum expectation value of the scalar field. We solve under the static and spherically symmetric ansatz the field equations of the SU (2) Yang-Mills theory coupled to a single adjoint scalar field whose radial degree of freedom is eliminated. We show that the solution can be identified with the gauge field configuration of a magnetic monopole with a minimum magnetic charge in the massive Yang-Mills theory. Moreover, we compare the magnetic monopole of the massive Yang-Mills theory obtained in this way with the Wu-Yang magnetic monopole in the pure Yang-Mills theory and the 't Hooft-Polyakov magnetic monopole in the Georgi-Glashow gauge-scalar model.
Lattice construction of Cho–Faddeev–Niemi decomposition and gauge-invariant monopole
Physics Letters B, 2006
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.
On Nonexistence of Magnetic Charge in Pure Yang-Mills Theories
Journal of High Energy Physics, 2002
We prove that magnetic charge does not exist as a physical observable on the physical Hilbert space of the pure SU (2) gauge theory. The abelian magnetic monopoles seen in lattice simulations are then interpreted as artifacts of gauge fixing. The apparent physical scaling properties of the monopole density in the continuum limit observed on the lattice are attributed to the correct scaling properties of physical objects-magnetic vortices, as first argued by Greensite et. al. We can show that a local gauge transformation of a certain type can "create" abelian monopole-antimonopole pairs along magnetic vortices. This gauge transformation exists in pure SU (N) gauge theory at any N .
Toward gauge independent study of confinement in SU(3) Yang-Mills theory
Dual superconductivity is believed to be a promising mechanism for quark confinement and has been investigated on a lattice effectively by a particular gauge called the maximal Abelian (MA) gauge. We propose a new formulation of SU(3) Yang-Mills theory on a lattice based on a non-linear change of variables where the new field variables are expected to reduce to those of the Cho-Faddeev-Niemi-Shabanov decomposition in the continuum limit. By introducing a new variable, say color field, carrying the color direction with it, this formulation enables us to restore and maintain color symmetry that was lost in the conventional MA gauge due to the naive separation of the gauge potential into diagonal and off-diagonal components. An advantage of this formulation is that we can define gaugeinvariant magnetic monopoles without relying on specific gauges to investigate quark confinement from the viewpoint of dual superconductivity. In this talk, we will present the relevant lattice formulation to realize the above advantages and preliminary results of numerical simulations to demonstrate the validity of this formulation. This SU(3) formulation is an extension of the SU(2) version already proposed by us in the previous conference.
Monopoles at finite volume and temperature in SU(2) lattice gauge theory
Physics Letters B - PHYS LETT B, 1996
We resolve a discrepancy between the SU(2) spatial string tension at finite temperature, and the value obtained by monopoles in the maximum Abelian gauge. Previous work had incorrectly omitted a term due to Dirac sheets. When this term is included, the monopole and full SU(2) determinations of the spatial string tension agree to within the statistical errors of the monopole calculation.
Abelian magnetic-monopole condensate in lattice gauge theory
Il Nuovo Cimento A, 1993
We investigate the monopole condensate in lattice gauge theory. We find that the monopole condensate in SU(2) lattice gauge theory in the maximal Abelian gauge behaves as in lattice electrodynamics. We argue that the monopole condensate is an order parameter for confinement, and find an evidence for the dual color superconductor hypothesis.