Remark on the BRST symmetry in the Gribov-Zwanziger theory

Capri, M. A. L.; Gomez, A. J.; Guimaraes, M. S.; Lemes, V. E. R.; Sorella, S. P.; Tedesco, D. G.

doi:10.1103/physrevd.82.105019

Cited by 58 publications

(71 citation statements)

References 34 publications

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“…However, beyond perturbation theory, gauge conditions like the Landau-gauge condition (6) have no longer a unique solution for a given configuration. There are several explicit examples illustrating this fact [18,[45][46][47][48]. Such independent solutions are called Gribov copies, and the associated ambiguity of the gauge condition is termed the Gribov-Singer ambiguity [18,19].…”

Section: Non-perturbative Gauge-fixing and Gribov Copiesmentioning

confidence: 99%

“…Indeed, there are at most two independent renormalization factors [2,185], which can be chosen, e. g., to be the one of the running coupling and the wave-function renormalization of the ghost 48 . Furthermore, in dimensions lower than four all renormalization constants, and thus correlation functions, are finite, though still some loop-graphs are divergent and require regularization [174].…”

Section: Renormalizationmentioning

confidence: 99%

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Gauge bosons at zero and finite temperature

2013

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Gauge theories of the Yang-Mills type are the single most important building block of the standard model of particle physics and beyond. They are an integral part of the strong and weak interactions, and in their Abelian version of electromagnetism. Since Yang-Mills theories are gauge theories their elementary particles, the gauge bosons, cannot be described without fixing a gauge. Therefore, to obtain their properties a quantized and gauge-fixed setting is necessary.Beyond perturbation theory, gauge-fixing in non-Abelian gauge theories is obstructed by the Gribov-Singer ambiguity, which requires the introduction of non-local constraints. The construction and implementation of a method-independent gauge-fixing prescription to resolve this ambiguity is the single most important first step to describe gauge bosons beyond perturbation theory. Proposals for such a procedure, generalizing the perturbative Landau gauge, are described here. Their implementation are discussed for two example methods, lattice gauge theory and the quantum equations of motion.After gauge-fixing, it is possible to study gauge bosons in detail. The most direct access is provided by their correlation functions. The corresponding two-and three-point correlation functions are presented at all energy scales. These give access to the properties of the gauge bosons, like their absence from the asymptotic physical state space, particle-like properties at high energies, and the running coupling. Furthermore, auxiliary degrees of freedom are introduced during gauge-fixing, and their properties are discussed as well. These results are presented for two, three, and four dimensions, and for various gauge algebras.Finally, the modifications of the properties of gauge bosons at finite temperature are presented. Evidence is provided that these reflect the phase structure of Yang-Mills theory. However, it is found that the phase transition is not deconfining the gauge bosons, although the bulk thermodynamical behavior is of a Stefan-Boltzmann type. The resolution of this apparent contradiction is also presented. In addition, this resolution provides an explicit and constructive solution to the Linde problem.Thus, the technical and conceptual framework presented here can be taken as a basis how to determine correlation functions in Yang-Mills theory, therefore opening up the avenue to investigate theories of direct practical relevance. The status of this effort will be briefly described, alongside with connections to other approaches to Yang-Mills theory beyond perturbation theory.

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Section: Non-perturbative Gauge-fixing and Gribov Copiesmentioning

confidence: 99%

Section: Renormalizationmentioning

confidence: 99%

Gauge bosons at zero and finite temperature

2013

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“…In fact this relation has been explored in many works [22][23][24][25][26][27][28]. The idea is that confined degrees of freedom are described by an effective action with a BRST-breaking soft term.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics of an exactly solvable confining quark model

2015

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The grand partition function of a model of confined quarks is exactly calculated at arbitrary temperatures and quark chemical potentials. The model is inspired by a softly BRST-broken version of QCD and possesses a quark mass function compatible with nonperturbative analyses of lattice simulations and Dyson-Schwinger equations. Even though the model is defined at tree level, we show that it produces a nontrivial and stable thermodynamic behaviour at any temperature or chemical potential. Results for the pressure, the entropy and the trace anomaly as a function of the temperature are qualitatively compatible with the effect of nonperturbative interactions as observed in lattice simulations. The finite density thermodynamics is also shown to contain nontrivial features, being far away from an ideal gas picture.

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“…As in the case of the Gribov-Zwanziger action [1,3,4,5,13,27,28,29,30,31,32], the local action S exhibits a soft breaking of the BRST symmetry, namely…”

Section: Identifying the Local Classical Starting Actionmentioning

confidence: 99%

Study of the all orders multiplicative renormalizability of a local confining quark action in the Landau gauge

2015

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The inverse of the Faddeev-Popov operator plays a pivotal role within the Gribov-Zwanziger approach to the quantization of Euclidean Yang-Mills theories in Landau gauge. Following a recent proposal [1], we show that the inverse of the Faddeev-Popov operator can be consistently coupled to quark fields. Such a coupling gives rise to a local action while reproducing the behaviour of the quark propagator observed in lattice numerical simulations in the non-perturbative infrared region. By using the algebraic renormalization framework, we prove that the aforementioned local action is multiplicatively renormalizable to all orders.

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Remark on the BRST symmetry in the Gribov-Zwanziger theory

Cited by 58 publications

References 34 publications

Gauge bosons at zero and finite temperature

Gauge bosons at zero and finite temperature

Thermodynamics of an exactly solvable confining quark model

Study of the all orders multiplicative renormalizability of a local confining quark action in the Landau gauge

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