Electric-magnetic asymmetry of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>A</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math>condensate and the phases of Yang-Mills theory

Chernodub, M. N.; Ilgenfritz, E. M.

doi:10.1103/physrevd.78.034036

Cited by 37 publications

(108 citation statements)

References 34 publications

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“…This also implies that the electric-magnetic asymmetry observed [431,432] in dimension-two gluon condensates [433] at finite temperature is driven just by the electric sector [249]. Only the soft electric part is then left.…”

Section: Intermediate Momenta and Temperaturesmentioning

confidence: 90%

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: Intermediate Momenta and Temperaturesmentioning

confidence: 90%

Gauge bosons at zero and finite temperature

2013

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“…In the works [49,50], the relation was explored between this condensate and magnetic degrees of freedom, which are generally believed to play an important role for confinement. Recently, this was further investigated by looking at the electric and magnetic components of A 2 at finite temperature, hinting towards an interesting connection with the phase diagram [70].…”

Section: An Important Asset In the Computation D(pmentioning

confidence: 99%

“…This condensate then made its appearance in a variety of works, see e.g. [22,[62][63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78][79]. In the works [49,50], the relation was explored between this condensate and magnetic degrees of freedom, which are generally believed to play an important role for confinement.…”

Section: An Important Asset In the Computation D(pmentioning

confidence: 99%

Indirect lattice evidence for the refined Gribov-Zwanziger formalism and the gluon condensate⟨A2⟩in the Landau gauge

2010

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We consider the gluon propagator D(p 2 ) at various lattice sizes and spacings in the case of pure SU(3) Yang-Mills gauge theories using the Landau gauge fixing. We discuss a class of fits in the infrared region in order to (in)validate the tree level analytical prediction in terms of the (Refined) Gribov-Zwanziger framework. It turns out that an important role is played by the presence of the widely studied dimension two gluon condensate A 2 . Including this effect allows to obtain an acceptable fit up to 1á 1.5 GeV, while corroborating the Refined Gribov-Zwanziger prediction for the gluon propagator. We also discuss the infinite volume extrapolation, leading to the estimate D(0) = 8.3 ± 0.5 GeV −2 . As a byproduct, we can also provide the prediction g 2 A 2 ≈ 3 GeV 2 obtained at the renormalization scale µ = 10 GeV.

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“…Necessarily it cannot diverge as divergences at finite T are the same as for T = 0, hence this asymmetry is in principle finite and can be computed without renormalization, for all temperatures. The authors of [12] found that the high-temperature behavior of the asymmetry had no surprises, following a power law as can be guessed from general thermodynamic arguments. For the low-temperature behavior, however, one would expect an exponential fall-off with the lowest glueball mass in the exponent, ∆ ∼ e −m gl T .…”

Section: Introductionmentioning

confidence: 99%

“…The dimension 2 gluon condensate A 2 µ in pure Yang-Mills theory has been proposed in [1,2], and it has been investigated in different ways since then [3,4,5,6,7,8,9,10,11,12,13,14].…”

Section: Introductionmentioning

confidence: 99%

Asymmetry of the dimension-two gluon condensate: The zero temperature case

Vercauteren

Verschelde

2009

Phys. Rev. D

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We provide an algebraic study of the local composite operators A µ A ν − δ µν d A 2 κ and A 2 µ , with d = 4 the spacetime dimension. We prove that these are separately renormalizable to all orders in the Landau gauge. This corresponds to a renormalizable decomposition of the operator A µ A ν into its trace and traceless part. We present explicit results for the relevant renormalization group functions to three loop order, accompanied with various tests of these results. We then develop a formalism to determine the zero temperature effective potential for the corresponding condensates, and recover the already known result for A 2 µ 0, together with A µ A ν − δ µν d A 2 κ = 0, a nontrivial check that the approach is consistent with Lorentz symmetry. The formalism is such that it is readily generalizable to the finite temperature case, which shall allow a future analytical study of the electric-magnetic symmetry of the A 2 µ condensate, which received strong evidence from recent lattice simulations by Chernodub and Ilgenfritz, who related their results to 3 regions in the Yang-Mills phase diagram.

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Electric-magnetic asymmetry of theA2condensate and the phases of Yang-Mills theory

Cited by 37 publications

References 34 publications

Gauge bosons at zero and finite temperature

Gauge bosons at zero and finite temperature

Indirect lattice evidence for the refined Gribov-Zwanziger formalism and the gluon condensate⟨A2⟩in the Landau gauge

Asymmetry of the dimension-two gluon condensate: The zero temperature case

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