New descriptions of lattice SU(N) Yang–Mills theory towards quark confinement (original) (raw)
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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.
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.
Discriminating between two reformulations of SU(3) Yang-Mills theory on a lattice
AIP Conference Proceedings, 2016
In oder to investigate quark confinement, we give a new reformulation of the SU(N) Yang-Mills theory on a lattice and present the results of the numerical simulations of the SU(3) Yang-Mills theory on a lattice. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the "Abelian" dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc.
Monopole condensation and quark confinement in a weak coupling SU(N) lattice gauge model
Nuclear Physics B, 1979
We present a model of SU(N) lattice Yang-Mills theory which exhibits asymptotic freedom and permanent quark confinement simultaneously. We argue that in the limit of vanishing bare gauge-coupling constant, the model is approximately mapped by a duality transformation to the confining phase of a Z(N) lattice gauge model. Existence of the continuum limit with the vanishingly small bare coupling constant (asymptotic freedom) requires us to make the duality map at the critical point of the Z(N) model. The mechanism of quark confinement is the condensation of magnetic monopoles and associated vortex strings which are topologically characterized by Z(N) group structure.
Monopoles, vortices and confinement in SU(3) lattice gauge theory
Nuclear Physics B - Proceedings Supplements, 2001
We present results for the heavy quark potential computed in SU(3) from magnetic monopoles and from center vortices. The monopoles are identified after fixing SU(3) lattice configurations to the maximal abelian gauge. The center vortices are identified after using an indirect center gauge fixing scheme which we describe for SU(3). Z(3) center vortices are extracted and used to compute the potential. The values of the string tensions from monopoles and vortices are compared to the full SU(3) string tension.
Quark Confinement in SU(3)Yang-Mills gauge theory
Soryushiron Kenkyu Electronics, 2000
We outline a derivation of the area law of the Wilson loop in SU(3) Yang-Mills theory in the maximal Abelian gauge (The detailed exposition will be given in a forthcoming article). This derivation is performed within the reformulation of the Yang-Mills theory recently proposed by one of the authors. To this end, we extend a non-Abelian Stokes theorem to SU(3) by making use of the coherent state representation on the coset space SU(3)/(U(1)×U(1)) = F 2 , the flag space. Our results suggest that the fundamental quark is confined if G = SU(3) is broken by partial gauge fixing into H = U(2) rather than U(1) × U(1). An origin of the area law is related to the geometric phase of the Wilczek-Zee holonomy for U(2). Abelian dominance and magnetic monopole dominance are immediate byproduct of these results.
Type of dual superconductivity for the SU(2) Yang–Mills theory
The European Physical Journal C, 2019
We investigate the type of dual superconductivity responsible for quark confinement. For this purpose, we solve the field equations of the U(1) gauge-scalar model to obtain a single static vortex solution in the whole range without restricting to the long-distance region. Then we use the resulting magnetic field of the vortex to fit the gauge-invariant chromoelectric field connecting a pair of quark and antiquark which was measured by numerical simulations for SU(2) Yang–Mills theory on a lattice. This result improves the accuracy of the fitted value for the Ginzburg–Landau parameter to reconfirm the type I dual superconductivity for quark confinement which was claimed by preceding works based on the fitting using the Clem ansatz. Moreover, we calculate the Maxwell stress tensor to obtain the distribution of the force around the flux tube. This result suggests that the attractive force acts among chromoelectric flux tubes, in agreement with the type I dual superconductivity.
Confinement and the vortex vacuum of SU (2) lattice gauge theory
The vortex theory which emerges from SU(2) lattice gauge theory by center projection is briefly reviewed. In this vortex picture, quark confinement is due to percolating (closed) vortices which are randomly linked to the Wilson loop. The deconfinement phase transition appears as a de-percolation phase transition.
Confinement of quarks in higher representations in view of dual superconductivity
Proceedings of The 36th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2018), 2019
Dual superconductor picture is one of the most promising scenarios for quark confinement. We have proposed a new formulation of Yang-Mills theory on the lattice so that the so-called restricted field obtained from the gauge-covariant decomposition plays the dominant role in quark confinement. This framework improves the Abelian projection in the gauge-independent manner. For quarks in the fundamental representation, we have demonstrated some numerical evidences for the dual superconductivity. However, it is known that the expected behavior of the Wilson loop in higher representations cannot be reproduced if the restricted part of the Wilson loop is extracted by adopting the Abelian projection or the field decomposition naively in the same way as in the fundamental representation. In this talk, therefore, we focus on confinement of quarks in higher representations. By virtue of the non-Abelian Stokes theorem for the Wilson loop operator, we propose suitable operators constructed from the restricted field only in the fundamental representation to reproduce the correct behavior of the original Wilson loop in higher representations. Moreover, we perform lattice simulations to measure the static potential for quarks in higher representations using the proposed operators. We find that the proposed operators well reproduce the expected behavior of the original Wilson loop average, which overcomes the problem that occurs in naively applying Abelian-projection to the Wilson loop operator for higher representations.