Thermodynamics of the Yang-Mills gas

Harrington, Barry J.; Shepard, Harvey K.

doi:10.1103/physrevd.18.2990

Cited by 78 publications

(106 citation statements)

References 24 publications

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“…There are two known generalizations of instantons at non-zero temperatures. One is the periodic instanton of Harrington and Shepard [54] studied in detail in ref. [52].…”

Section: Dyons and Calorons With Non-trivial Holonomymentioning

confidence: 99%

Instantons at work

Diakonov

2003

Progress in Particle and Nuclear Physics

352

506

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The aim of this review is to demonstrate that there exists a coherent picture of strong interactions, based on instantons. Starting from the first principles of Quantum Chromodynamics -via the microscopic mechanism of spontaneous chiral symmetry breakingone arrives to a quantitative description of the properties of light hadrons, with no fitting parameters. The discussion of the importance of instanton-induced interactions in soft high-energy scattering is new.

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“…There are two known generalizations of instantons at non-zero temperatures. One is the periodic instanton of Harrington and Shepard [54] studied in detail in ref. [52].…”

Section: Dyons and Calorons With Non-trivial Holonomymentioning

confidence: 99%

Instantons at work

Diakonov

2003

Progress in Particle and Nuclear Physics

352

506

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“…1. When ρ ≪ b no difference would be seen with the action density of the Harrington-Shepard solution [1], the gauge field is nevertheless vastly different, as follows from the fact that within the confines of the peak there are n locations where two of the eigenvalues of the Polyakov loop coincide [13,14,15]. When, on the other hand, constituents of equal charge come together (which requires |Q| > 1) an extended core structure ap- Figure 1.…”

Section: Introductionmentioning

confidence: 99%

“…We first briefly summarize the essential features of instantons at finite temperature T , socalled calorons [1]. A non-trivial Polyakov loop at spatial infinity (the so-called holonomy), which in some sense plays the role of a Higgs field, reveals the monopole constituent nature of these calorons [2,3,4].…”

Section: Introductionmentioning

confidence: 99%

Calorons with non-trivial holonomy on and off the lattice

Bruckmann

Ilgenfritz

Martemyanov

et al. 2005

Nuclear Physics B - Proceedings Supplements

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“…The Polyakov line at the boundary is then the trace of the holonomy L(x) = caloron solutions appear once a non-trivial holonomy P(x) at |x| → ∞ is admitted. These solutions differ from the 't Hooft periodic instantons employed for the standard semi-classical approach at finite temperatures [3][4][5]. The latter solutions have trivial holonomy i.e.…”

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confidence: 99%

SU(2) lattice gauge theory at non-zero temperature with fixed holonomy boundary condition

Ilgenfritz

Martemyanov

Müller-Preusskaer

et al. 2001

Nuclear Physics B - Proceedings Supplements

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We study SU (2) lattice gauge theory at T > 0 in a finite box with fixed holonomy value at the spatial boundary. We search for (approximate) classical solutions of the lattice field equations and find in particular the dissociated calorons recently discussed by van Baal and collaborators.The quark confinement has not yet found a satisfactory explanation. Several models are under consideration. The dual superconductor scenario views confinement as a dual Meissner effect due to the condensation of Abelian monopoles. An alternative promising approach is based on the center-vortex dominance picture. On the other hand there is the semiclassical approach based on instanton solutions. It provides successful phenomenology for many phenomena in hadron physics. Unfortunately, instanton gas or liquid models fail to explain confinement. The question arises, whether other extended classical objects -e.g. monopoles or dyons -could be suited to describe confinement within a semi-classical approach.We consider SU (2) lattice gauge theory at finite temperature with periodic boundary conditions characterized additionally by a non-trivial holonomy P(x) at the spatial boundary. The Polyakov line at the boundary is then the trace of the holonomy L(x) = caloron solutions appear once a non-trivial holonomy P(x) at |x| → ∞ is admitted. These solutions differ from the 't Hooft periodic instantons employed for the standard semi-classical approach at finite temperatures [3][4][5]. The latter solutions have trivial holonomy i.e. P(x) → 1 for |x| → ∞.The most interesting feature of the new calorons is the fact that monopole constituents of an instanton can become explicit as degrees of freedom [7,8]. They carry magnetic charge (in fact, they are BPS monopoles [6]) and 1/N color units of topological charge. Being part of classical solutions of the Euclidean field equations, one can hope that the instanton constituents can play an independent role in the semiclassical analysis of T = 0 Yang-Mills theory (and of full QCD).Here we present an exploratory study where we have searched for characteristic differences between the two phases as far as semiclassical background fields are concerned. The latter become visible in the result of cooling.We have fixed during the simulation and under cooling the boundary time-like link variables in order to keep a certain value of P(x) = P ∞ everywhere on the spatial surface of the system while conserving periodicity. In this case, the influence of the respective phase, that we want to describe, is twofold : (i) the cooling starts from genuine thermal Monte Carlo gauge field configurations,

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Thermodynamics of the Yang-Mills gas

Cited by 78 publications

References 24 publications

Instantons at work

Instantons at work

Calorons with non-trivial holonomy on and off the lattice

SU(2) lattice gauge theory at non-zero temperature with fixed holonomy boundary condition

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