Magnetic monopoles and topology of Yang-Mills theory in Polyakov gauge

Quandt, Markus; Reinhardt, Hugo; Schäfke, A.

doi:10.1016/s0370-2693(98)01547-0

Cited by 12 publications

(9 citation statements)

References 11 publications

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“…In this case the surface S p surrounding the wall D p consists of several connected parts. If the wall defect does not extent over Ì 3 every part of S p has no boundary and we get the above quantization condition, see also [20]. If the wall-defect extends over Ì 3 then each part of S p also extends over Ì 3 .…”

mentioning

confidence: 63%

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SU(N)-gauge theories in Polyakov gauge on the torus

Ford¹,

Tok²,

Wipf³

1999

Physics Letters B

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We investigate the Abelian projection with respect to the Polyakov loop operator for SU (N ) gauge theories on the four torus. The gauge fixed A 0 is time-independent and diagonal. We construct fundamental domains for A 0 . In sectors with nonvanishing instanton number such gauge fixings are always singular. The singularities define the positions of magnetically charged monopoles, strings or walls. These magnetic defects sit on the Gribov horizon and have quantized magnetic charges. We relate their magnetic charges to the instanton number.In the absence of dynamical fermions the relevant observables for confinement studies are products of Wilson-loops [1]. At finite temperature T = 1/β the gauge potentials in the functional integral are periodic in Euclidean time i.e.and one may use Polyakov loops [2] P ( x) = tr (P(β, x)), where P(x 0 , x) = P exp ias order parameters for confinement. Below we set P(β, x) ≡ P( x). We shall follow the strategy put forward by G. 't Hooft [3] who considered Yang-Mills theories on a Euclidean space-time torus Ì 4 . The torus provides a gauge invariant infrared cut-off. Its non-trivial topology gives rise to a non-trivial structure in the space of Yang-Mills fields which yields additional information on the possible phases of Yang-Mills theories.

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mentioning

confidence: 63%

“…By noting that the fundamental weights are dual to the simple roots we see at once that Q M must be proportional to α (σ) . With the quantization conditions (20) we arrive at…”

mentioning

confidence: 99%

SU(N)-gauge theories in Polyakov gauge on the torus

Ford¹,

Tok²,

Wipf³

1999

Physics Letters B

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“…This implies that the wave functional describing such a state is different for gauge field configurations which belong to O + and O − respectively, and which therefore are connected by gauge transformations such as ω − in Eq. (42). These symmetry considerations apply equally well when adjoint matter is coupled to the gauge fields.…”

Section: Polyakov-loops and Center Symmetrymentioning

confidence: 81%

“…The above equation shows that, in axial gauge, a single instanton contains a north (P = 1) and south pole singularity (P = −1) at its center and at infinity respectively. More generally it has be shown [41,42,43] that the topological charge ν of a field configuration is given by the difference of the net northern and southern charge…”

Section: Monopole Dynamicsmentioning

confidence: 99%

Compact Variables and Singular Fields in QCD

Lenz

Woerlen

2001

At the Frontier of Particle Physics

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Subject of our investigations is QCD formulated in terms of physical degrees of freedom. Starting from the Faddeev-Popov procedure, the canonical formulation of QCD is derived for static gauges. Particular emphasis is put on obstructions occurring when implementing gauge conditions and on the concomitant emergence of compact variables and singular fields. A detailed analysis of non-perturbative dynamics associated with such exceptional field configurations within Coulomb-and axial gauge is described. We present evidence that compact variables generate confinement-like phenomena in both gauges and point out the deficiencies in achieving a satisfactory non-perturbative treatment concerning all variables. Gauge fixed formulations are shown to constitute also a useful framework for phenomenological studies. Phenomenological insights into the dynamics of Polyakov loops and monopoles in confined and deconfined phases are presented within axial gauge QCD.

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“…In non-Abelian gauge theories, there might be topological obstructions to implementing this gauge [22,23]; such defects are, however, associated with non-trivial (periodic) boundary conditions in the time direction. For static configurations, no such obstructions exists and the Weyl gauge may always be attained; the residual gauge freedom consists of all time-independent gauge rotations.…”

Section: A the Classical String Solutionsmentioning

confidence: 99%

Quantum energies of strings in a ()-dimensional gauge theory

Graham

Quandt

Schröder³

et al. 2006

Nuclear Physics B

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We study classically unstable string type configurations and compute the renormalized vacuum polarization energies that arise from fermion fluctuations in a 2+1 dimensional analog of the standard model. We then search for a minimum of the total energy (classical plus vacuum polarization energies) by varying the profile functions that characterize the string. We find that typical string configurations bind numerous fermions and that populating these levels is beneficial to further decrease the total energy. Ultimately our goal is to explore the stabilization of string type configurations in the standard model through quantum effects.We compute the vacuum polarization energy within the phase shift formalism which identifies terms in the Born series for scattering data and Feynman diagrams. This approach allows us to implement standard renormalization conditions of perturbation theory and thus yields the unambiguous result for this non-perturbative contribution to the total energy.

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Magnetic monopoles and topology of Yang-Mills theory in Polyakov gauge

Cited by 12 publications

References 11 publications

SU(N)-gauge theories in Polyakov gauge on the torus

SU(N)-gauge theories in Polyakov gauge on the torus

Compact Variables and Singular Fields in QCD

Quantum energies of strings in a ()-dimensional gauge theory

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