The Gribov problem in presence of background field for SU(2) Yang–Mills theory

Canfora, Fabrizio; Hidalgo, Diego; Pais, P.

doi:10.1016/j.physletb.2016.10.024

Cited by 11 publications

(19 citation statements)

References 74 publications

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“…Now that we have introduced a background gauge invariant Gribov-Zwanziger action in the Landau-DeWitt gauge, summarized in (33), and have explicitly shown how to work with this action at zero temperature for at least the phenomenologically relevant constant Abelian backgrounds in the temporal direction, we can now progress in future work towards the finite temperature analysis, of relevance for probing the deconfinement transition using functional tools. Doing so, we can correct the earlier analyses of [21,22] where the non-background gauge invariant Gribov-Zwanziger action was employed, with the here discussed spontaneous Lorentz symmetry breaking that is now averted.…”

Section: Discussionmentioning

confidence: 94%

“…In this Letter, we revisit in Section 2 the problem of Gribov copies in the Landau-DeWitt gauge and try to derive a Gribov-Zwanziger action. Although succeeding in the latter, we identify a major drawback, shared with the conjectured action in [21,22]: even at zero temperature, a nonzero value of a Lorentz symmetry breaking background is energetically favoured. The problem is traced back to the lack of background gauge invariance and, underlyingly, of BRST invariance of the original Gribov-Zwanziger approach.…”

Section: Introductionmentioning

confidence: 81%

“…It is, however, not at all straightforward to use the above-mentioned symmetries in combination with the Gribov-Zwanziger formalism. In fact, in [21,22] a trial Gribov-Zwanziger action was employed in presence of a background, inspired by [20]. However, a similar observation holds true at T = 0 when properly 4 using that background Gribov-Zwanziger action: the ground state would favour a nonzero A.…”

Section: Lack Of Background Gauge Invariance and A Symmetric Approachmentioning

confidence: 98%

“…In the presence of backgrounds, seminal work is [20], based on which a background version of the Gribov-Zwanziger effective action was proposed and used to probe non-perturbative finite temperature dynamics in [21,22].…”

Section: Introductionmentioning

confidence: 99%

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Gauge copies in the Landau–DeWitt gauge: A background invariant restriction

Dudal

Vercauteren²

2018

Physics Letters B

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The Landau background gauge, also known as the Landau-DeWitt gauge, has found renewed interest during the past decade given its usefulness in accessing the confinementdeconfinement transition via the vacuum expectation value of the Polyakov loop, describable via an appropriate background. In this Letter, we revisit this gauge from the viewpoint of it displaying gauge (Gribov) copies. We generalize the Gribov-Zwanziger effective action in a BRST and background invariant way; this action leads to a restriction on the allowed gauge fluctuations, thereby eliminating the infinitesimal background gauge copies. The explicit background invariance of our action is in contrast with earlier attempts to write down and use an effective Gribov-Zwanziger action. It allows to address certain subtleties arising in these earlier works, such as a spontaneous and thus spurious Lorentz symmetry breaking, something which is now averted. * david.dudal@kuleuven.be † vercauterendavid@dtu.edu.vn

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Section: Discussionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 81%

Section: Lack Of Background Gauge Invariance and A Symmetric Approachmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Gauge copies in the Landau–DeWitt gauge: A background invariant restriction

Dudal

Vercauteren²

2018

Physics Letters B

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“…We then selected the (unique at the considered order) scheme in which the computed (tree level) complex conjugate poles match those lattice values. As such, we have identified a specific renormalization scheme to treat the divergences at zero temperature (the case considered here), upon which we can build in future work to discuss the interplay of condensates and Gribov gap equation with the temperature, with as ultimate goal to find out whether the GZ quantization can capture some essentials of the QCD thermodynamics and phase transitions, thereby putting on firmer footing preceding studies like [122][123][124][125][126][127].…”

Section: Resultsmentioning

confidence: 99%

The BRST-invariant vacuum state of the Gribov–Zwanziger theory

et al. 2019

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We revisit the effective action of the Gribov-Zwanziger theory, taking into due account the BRST symmetry and renormalization (group invariance) of the construction. We compute at one loop the effective potential, showing the emergence of BRST-invariant dimension 2 condensates stabilizing the vacuum. This paper sets the stage at zero temperature, and clears the way to studying the Gribov-Zwanziger gap equations, and particularly the horizon condition, at finite temperature in future work. I. INTRODUCTIONUp until now, quark and gluon confinement has not been rigorously proven. It is well known that the perturbative formalism fails for non-Abelian gauge theories at low energy, since the coupling constant g 2 is strong. To get reliable results in the infrared (IR) in the continuum formulation, non-perturbative methods are needed. For an overview of such methods and obtained results, let us refer for example to . Notice that the continuum formulation requires gauge fixing, in which case lattice analogues of dedicated gauge fixings can be a powerful ally giving complementary insights, see for some relevant works in this area.Motivated by this, a number of studies over the past decade have focused on the gluon, quark and also ghost propagator in the infrared region, where color degrees of freedom are confined. Although these objects are unphysical by themselves -being gauge variant -they are nevertheless the basic building blocks, next to the interaction vertices, entering gauge-invariant objects directly linked to physically relevant quantities such as the spectrum, decay constants, critical exponents and temperatures, etc.One particular way to deal with non-perturbative physics at the level of elementary degrees of freedom is by dealing with the Gribov issue [21,80]: the fact that there is no unique way of selecting one representative configuration of a given gauge orbit in covariant gauges [81]. As there is also no rigourous way to deal properly with the existence of gauge copy modes in the path integral quantization procedure, in this paper we will use a well-tested formalism available to deal with the issue, which is known as the Gribov-Zwanziger (GZ) formalism: a restriction of the path integral to a smaller subdomain of gauge fields [80,82,83].This approach was first proposed for the Landau and the Coulomb gauges . It long suffered from a serious drawback: its concrete implementation seemed to be inconsistent with BRST (Becchi-Rouet-Stora-Tyutin [84-86]) invariance of the gauge-fixed theory, which clouded its interpretation as a gauge (fixed) theory. Only more recently was it realized by some of us and colleagues how to overcome this complication to get a BRST-invariant restriction of the gauge path integral . As a bonus, the method also allowed the generalization of the GZ approach to the linear covariant gauges, amongst others [36,37,43,45].Another issue with the original GZ approach was that some of its major leading-order predictions did not match the corresponding lattice output. Indeed, in the case of the...

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