Infrared singularities in Landau gauge Yang-Mills theory

Alkofer, Reinhard; Huber, Markus Q.; Schwenzer, Kai

doi:10.1103/physrevd.81.105010

Cited by 98 publications

(130 citation statements)

References 76 publications

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“…(ii) A similar analysis was performed in [101], for one soft and two hard external momenta, finding a softer divergence, of the type (p 2 ) 1−2κ . (iii) A study with a more complete tensorial structure was carried out in [102], where the transverse parts of the three-gluon vertex turned out to be very mildly divergent, and with no appreciable impact on the gluon and ghost SDEs.…”

Section: Discussionmentioning

confidence: 99%

Unified description of seagull cancellations and infrared finiteness of gluon propagators

Aguilar¹,

Binosi²,

Figueiredo³

et al. 2016

Phys. Rev. D

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We present a generalized theoretical framework for dealing with the important issue of dynamical mass generation in Yang-Mills theories, and, in particular, with the infrared finiteness of the gluon propagators, observed in a multitude of recent lattice simulations. Our analysis is manifestly gauge-invariant, in the sense that it preserves the transversality of the gluon self-energy, and gauge-independent, given that the conclusions do not depend on the choice of the gauge-fixing parameter within the linear covariant gauges. The central construction relies crucially on the subtle interplay between the Abelian Ward identities satisfied by the nonperturbative vertices and a special integral identity that enforces a vast number of 'seagull cancellations' among the oneand two-loop dressed diagrams of the gluon Schwinger-Dyson equation. The key result of these considerations is that the gluon propagator remains rigorously massless, provided that the vertices do not contain (dynamical) massless poles. When such poles are incorporated into the vertices, under the pivotal requirement of respecting the gauge symmetry of the theory, the terms comprising the Ward identities conspire in such a way as to still enforce the total annihilation of all quadratic divergences, inducing, at the same time, residual contributions that account for the saturation of gluon propagators in the deep infrared.

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Section: Discussionmentioning

confidence: 99%

Unified description of seagull cancellations and infrared finiteness of gluon propagators

Aguilar¹,

Binosi²,

Figueiredo³

et al. 2016

Phys. Rev. D

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show abstract

“…The essential point for the validity of this formula is that, because of the absence of other scales, the integral is dominated by the contributions around the external momenta 36 [185]. Since this in turn depends on the singularity structure of the propagators, and in general of the vertices [197], this yields that the integration turns, up to a constant pre-factor, into a map from the topology of the diagram to the exponent of the external momentum scale [200].…”

Section: Scaling Behaviormentioning

confidence: 99%

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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“…However, such comparisons have to be taken with a grain of salt, since it is known that lattice results depend on the details of the employed gauge fixing algorithm [10][11][12]. Also for functional methods several solutions can be obtained [13][14][15], but the correspondence between the solutions of one method to the ones of the other are not known. In addition, available lattice results are mostly limited to propagators in the vacuum and to the Landau gauge.…”

Section: Testing Truncations: Yang-mills Theory In Three Dimensionsmentioning

confidence: 99%

“…In four dimensions, a solution can be chosen by the renormalization condition for the ghost propagator [13][14][15]. Motivated by results from the functional renormalization group in four dimensions, where spurious divergences can be handled via tuning of a bare mass parameter [3], one can try and fix different values for the gluon propagator at zero momentum as an alternative way to handle spurious divergences.…”

Section: Testing Truncations: Yang-mills Theory In Three Dimensionsmentioning

confidence: 99%

An exploratory study of Yang-Mills three-point functions at non-zero temperature

Huber

2017

EPJ Web Conf.

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Abstract. Results for three-point functions of Landau gauge Yang-Mills theory at nonvanishing temperature are presented and compared to lattice results. It is found that the three-gluon vertex is enhanced for temperatures below the phase transition. At very low momenta it becomes negative for all temperatures. Furthermore, truncation effects in functional equations are discussed at the example of three-dimensional Yang-Mills theory for which a self-contained solution is presented.

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Infrared singularities in Landau gauge Yang-Mills theory

Cited by 98 publications

References 76 publications

Unified description of seagull cancellations and infrared finiteness of gluon propagators

Unified description of seagull cancellations and infrared finiteness of gluon propagators

Gauge bosons at zero and finite temperature

An exploratory study of Yang-Mills three-point functions at non-zero temperature

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