Extended Double Lattice BRST, Curci-Ferrari Mass and the Neuberger Problem

Ghiotti, M.; Smekal, Lorenz von; Williams, Anthony G.

doi:10.1063/1.2714366

Cited by 11 publications

(15 citation statements)

References 4 publications

(9 reference statements)

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“…We will demonstrate explicitly below that this zero can be regularized, however, by introducing a Curci-Ferrari mass m, as proposed in [9,10]. The gauge-fixing action S GF is thereby once more replaced by…”

Section: The Massive Curci-ferrari Model On the Latticementioning

confidence: 98%

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Decontracted double BRST symmetry on the lattice

2008

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We present the Curci-Ferrari model on the lattice. In the massless case the topological interpretation of this model with its double BRST symmetry relates to the Neuberger 0/0 problem which we extend to include the ghost/anti-ghost symmetric formulation of the non-linear covariant Curci-Ferrari gauges on the lattice. The introduction of a Curci-Ferrari mass term, however, serves to regulate the 0/0 indeterminate form of physical observables observed by Neuberger. While such a mass m decontracts the double BRST/anti-BRST algebra, which is well-known to result in a loss of unitarity, observables can be meaningfully defined in the limit m → 0 via l'Hospital's rule. At finite m the topological nature of the partition function used as the gauge fixing device seems lost. We discuss the gauge parameter ξ and mass m dependence of the model and show how both cancel when m ≡ m(ξ) is appropriately adjusted with ξ.

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Section: The Massive Curci-ferrari Model On the Latticementioning

confidence: 98%

“…In this paper we develop a full lattice formulation of the time-honored model by Curci and Ferrari with its decontracted double BRST/anti-BRST and ghost-mass term, as announced in [10]. After introducing the general setup for double BRST on the lattice in Sec.…”

Section: Introductionmentioning

confidence: 99%

Decontracted double BRST symmetry on the lattice

2008

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“…However, recently it has been proved [65] that the Curci-Ferrari model regularize this zero, gauge invariant correlators acquiring a definite expression for any non-zero mass. This allows for a non-perturbative construction of the BRST-invariant model on a lattice [66]. This is radically different to usual gauge theories where Neuberger's zero forbids such a construction [63].…”

Section: Introductionmentioning

confidence: 99%

Some Nonrenormalization Theorems in Curci–ferrari Model

Wschebor

2008

Int. J. Mod. Phys. A

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In the present letter, a particular form of Slavnov-Taylor identities for the Curci-Ferrari model is deduced. This model consist of Yang-Mills theory in a particular non-linear covariant gauge, supplemented with mass terms for gluons and ghosts. It can be used as a regularization for the Yang-Mills theory preserving simple Slavnov-Taylor identities. Employing these identities two nonrenormalization theorems are proved that reduce the number of independent renormalization factors from five to three. These new relations are verified by comparing to the already known three-loops renormalization factors. These relations include, as a particular case, the corresponding known identities in Yang-Mills theory in Landau gauge. 1

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“…Another way was put forward in Refs. [43,44,45] using the ghost/anti-ghost symmetric Curci-Ferrari gauges . There the argument used was that the Neuberger 0/0 problem could be extended to include such non-linear gauges with their extended double-BRST symmetry despite their quartic ghost self-interactions, which allow the introduction of a mass term for ghosts.…”

Section: Introductionmentioning

confidence: 99%

Enumerating Gribov copies on the lattice

2013

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In the modern formulation of lattice gauge-fixing, the gauge fixing condition is written in terms of the minima or stationary points (collectively called solutions) of a gauge-fixing functional. Due to the non-linearity of this functional, it usually has many solutions called Gribov copies. The dependence of the number of Gribov copies, n[U] on the different gauge orbits plays an important role in constructing the Faddeev-Popov procedure and hence in realising the BRST symmetry on the lattice. Here, we initiate a study of counting n[U] for different orbits using three complimentary methods: 1. analytical results in lower dimensions, and some lower bounds on n[U] in higher dimensions, 2. the numerical polynomial homotopy continuation method, which numerically finds all Gribov copies for a given orbit for small lattices, and 3. numerical minimisation ("brute force"), which finds many distinct Gribov copies, but not necessarily all. Because n for the coset SU(N_c)/U(1) of an SU(N_c) theory is orbit-independent, we concentrate on the residual compact U(1) case in this article and establish that n is orbit-dependent for the minimal lattice Landau gauge and orbit-independent for the absolute lattice Landau gauge. We also observe that contrary to a previous claim, n is not exponentially suppressed for the recently proposed stereographic lattice Landau gauge compared to the naive gauge in more than one dimension.Comment: 39 pages, 15 eps figures. Published version: minor changes onl

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Extended Double Lattice BRST, Curci-Ferrari Mass and the Neuberger Problem

Cited by 11 publications

References 4 publications

Decontracted double BRST symmetry on the lattice

Decontracted double BRST symmetry on the lattice

Some Nonrenormalization Theorems in Curci–ferrari Model

Enumerating Gribov copies on the lattice

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