Gribov-Zwanziger action in SU(2) maximally Abelian gauge with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:msub><mml:mrow /><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>Landau gauge

Gongyo, Shinya; Iida, Hidehiro

doi:10.1103/physrevd.89.025022

Cited by 21 publications

(43 citation statements)

References 49 publications

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“…For a vanishing background, this is precisely the original Gribov-Zwanziger construction [3,14,15], also applicable to the Coulomb gauge. More recently, it was also generalized to the SU(2) maximal Abelian gauge in [59]. Intuitively, it might be clear that the precise influence on the quantum dynamics by Gribov copies can strongly depend on the chosen background, given that Gribov copies are defined via the zero modes of the Faddeev-Popov operator of the chosen gauge condition, which itself explicitly depends on the chosen background.…”

Section: With T a The Infinitesimal Generators Of The Su(n)mentioning

confidence: 99%

Effect of the Gribov horizon on the Polyakov loop and vice versa

et al. 2015

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We consider finite-temperature SU(2) gauge theory in the continuum formulation, which necessitates the choice of a gauge fixing. Choosing the Landau gauge, the existing gauge copies are taken into account by means of the Gribov-Zwanziger quantization scheme, which entails the introduction of a dynamical mass scale (Gribov mass) directly influencing the Green functions of the theory. Here, we determine simultaneously the Polyakov loop (vacuum expectation value) and Gribov mass in terms of temperature, by minimizing the vacuum energy w.r.t. the Polyakov-loop parameter and solving the Gribov gap equation. Inspired by the Casimir energy-style of computation, we illustrate the usage of Zeta function regularization in finite-temperature calculations. Our main result is that the Gribov mass directly feels the deconfinement transition, visible from a cusp occurring at the same temperature where the Polyakov loop becomes nonzero. In this exploratory work we mainly restrict ourselves to the original Gribov-Zwanziger quantization procedure in order to illustrate the approach and the potential direct link between the vacuum structure of the theory (dynamical mass scales) and (de)confinement. We also present a first look at the critical temperature obtained from the refined Gribov-Zwanziger approach. Finally, a particular problem for the pressure at low temperatures is reported. a

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Section: With T a The Infinitesimal Generators Of The Su(n)mentioning

confidence: 99%

Effect of the Gribov horizon on the Polyakov loop and vice versa

et al. 2015

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“…There are two notable examples of gauge choices which also possess a Hermitean Faddeev-Popov operator: the maximal Abelian and Coulomb gauges. For such gauges, an explicit construction of the Gribov-Zwanziger action and its refinement was performed, see [48][49][50][51][52][53][54][55][56][57][58][59][60][61]. In spite of this fact, these gauges have their own peculiarities and the development of the refined Gribov-Zwanziger scenario for them is not at the same level as in the Landau gauge.…”

Section: The Gribov Problem In the Landau Gaugementioning

confidence: 99%

A non-perturbative study of matter field propagators in Euclidean Yang–Mills theory in linear covariant, Curci–Ferrari and maximal Abelian gauges

et al. 2017

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In this work, we study the propagators of matter fields within the framework of the refined GribovZwanziger theory, which takes into account the effects of the Gribov copies in the gauge-fixing quantization procedure of Yang-Mills theory. In full analogy with the pure gluon sector of the refined Gribov-Zwanziger action, a non-local long-range term in the inverse of the FaddeevPopov operator is added in the matter sector.

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“…The model we present in this talk has been recently studied numerically by Gongyo and Zwanziger [15]. The quantities studied in their paper were the expectation value of the Wilson loop, the massive gluon propagator and the order parameter (proportional to the integral over space of the PCSM field, U).…”

Section: Comments On Numerical Results and Finite Size Effectsmentioning

confidence: 99%

The Hadronic Spectrum and Confined Phase in (1+1)-Dimensional Massive Yang-Mills Theory

Cubero

2015

Proceedings of the 32nd International Symposium on Lattice Field Theory — PoS(LATTICE2014)

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Massive Yang-Mills theory is known to be renormalizable in 1+1 dimensions. The gluon mass is introduced by coupling the gauge field to an SU(N) principal chiral nonlinear sigma model. The proof of renormalizability relies on the asymptotic freedom of the sigma model. However, renormalization forces the gluon mass to infinity. The continuum theory is in a confined phase rather than a Higgs phase. The physical excitations of the system are hadron-like bound states of sigma model particles. We calculate the massive spectrum of meson-like bound states analytically, using the exact S-matrix of the sigma model. The baryon-like spectrum can be found in principle by solving a quantum mechanical N-body problem. We remark on the evidence for the confined phase found for SU(2) in recent lattice simulations by Gongyo and Zwanziger. Their simulations show evidence for a Higgs-like phase which seems to disappear with increasing volume, finding agreement with our analysis in the continuum.

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Gribov-Zwanziger action in SU(2) maximally Abelian gauge withU(1)3Landau gauge

Cited by 21 publications

References 49 publications

Effect of the Gribov horizon on the Polyakov loop and vice versa

Effect of the Gribov horizon on the Polyakov loop and vice versa

A non-perturbative study of matter field propagators in Euclidean Yang–Mills theory in linear covariant, Curci–Ferrari and maximal Abelian gauges

The Hadronic Spectrum and Confined Phase in (1+1)-Dimensional Massive Yang-Mills Theory

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