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| The '''QCD vacuum''' is the [[vacuum state]] of [[quantum chromodynamics]] (QCD). It is an example of a ''[[non-perturbative]]'' vacuum state, characterized by infinitely many non-vanishing [[condensate (quantum field theory)|condensate]]s such as the [[gluon condensate]] or the [[quark condensate]]. These condensates characterize the '''normal phase''' or the '''confined phase''' of [[quark matter]].
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| {{unsolved|physics|QCD in the non-[[Perturbation theory (quantum mechanics)|perturbative]] regime:
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| '''[[colour confinement|confinement]]'''. The equations of QCD remain unsolved at [[energy scale]]s relevant for describing [[Atomic nucleus|atomic nuclei]]. How does QCD give rise to the physics of [[Atomic nucleus|nuclei]] and [[hadron|nuclear constituents]]?}}
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| Another [[Vacuum state|field-theoretic vacuum]] is the [[QED vacuum]] of [[quantum electrodynamics]].
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| ==Symmetries and symmetry breaking== | | == Air Max 90 der kender mig personligt == |
| ===Symmetries of the QCD Lagrangian===
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| Like any [[theory of relativity|relativistic]] [[quantum field theory]], [[Quantum chromodynamics|QCD]] enjoys [[Poincaré group|Poincaré symmetry]] including the discrete symmetries [[CPT symmetry|CPT]] (each of which is realized). Apart from these space-time symmetries, it also has internal symmetries. Since QCD is an [[SU(3)]] [[gauge theory]], it has local SU(3) [[gauge symmetry]].
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| Since it has many [[flavour (particle physics)|flavour]]s of quarks, it has approximate flavour and [[chiral symmetry]]. This approximation is said to involve the '''chiral limit''' of QCD. Of these chiral symmetries, the [[baryon number]] symmetry is exact. Some of the broken symmetries include the axial U(1) symmetry of the flavour group. This is broken by the [[chiral anomaly]]. The presence of [[instanton]]s implied by this anomaly also [[strong CP problem|breaks CP symmetry]].
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| In summary, the QCD Lagrangian has the following symmetries:
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| *[[Poincaré symmetry]] and [[CPT symmetry|CPT]] invariance
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| *SU(3) local [[gauge symmetry]]
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| *approximate global SU(N<sub>f</sub>)XSU(N<sub>f</sub>) [[flavour (particle physics)|flavour]] [[chiral symmetry]] and the U(1) [[baryon number]] symmetry
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| The following classical symmetries are broken in the QCD Lagrangian:
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| *scale, i.e., [[conformal symmetry]] (through the [[scale anomaly]]), giving rise to [[asymptotic freedom]]
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| *the axial part of the U(1) [[flavour (particle physics)|flavour]] chiral symmetry (through the [[chiral anomaly]]), giving rise to the [[strong CP problem]].
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| ===Spontaneous symmetry breaking===
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| {{Main|Spontaneous symmetry breaking}}
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| | | </ul> |
| When the [[Hamiltonian (quantum mechanics)|Hamiltonian]] of a system (or the [[Lagrangian]]) has a certain symmetry, but the [[ground state]] (i.e., the [[vacuum#The quantum-mechanical vacuum|vacuum]]) does not, then one says that '''spontaneous symmetry breaking''' (SSB) has taken place.
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| A familiar example of SSB is in [[magnet|ferromagnetic materials]]. Microscopically, the material consists of [[atom]]s with a non-vanishing spin, each of which acts like a tiny bar magnet, i.e., a [[magnetic dipole]]. The Hamiltonian of the material, describing the interaction of neighbouring dipoles, is invariant under [[rotation]]s. At high temperature, there is no [[magnet]]ization of a large sample of the material. Then one says that the symmetry of the Hamiltonian is realized by the system. However, at low temperature, there could be an overall magnetization. This magnetization has a ''preferred direction'', since one can tell the north magnetic pole of the sample from the south magnetic pole. In this case, there is spontaneous symmetry breaking of the rotational symmetry of the Hamiltonian.
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| When a [[continuous symmetry]] is spontaneously broken, massless [[boson]]s appear, corresponding to the remaining symmetry. This is called the '''Goldstone phenomenon''' and the bosons are called [[Goldstone boson]]s.
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| ===Symmetries of the QCD vacuum===
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| The SU(N<sub>f</sub>) × SU(N<sub>f</sub>) chiral flavour symmetry of the QCD Lagrangian is broken in the [[vacuum state]] of the theory. The symmetry of the vacuum state is the diagonal SU(N<sub>f</sub>) part of the chiral group. The diagnostic for this is the formation of a non-vanishing [[chiral condensate]] <math>\langle\overline\psi_i\psi_i\rangle</math>, where ψ<sub>i</sub> is the quark field operator, and the flavour index '''i''' is summed. The [[Goldstone boson]]s of the symmetry breaking are the [[pseudoscalar (physics)|pseudoscalar]] [[meson]]s.
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| When N<sub>f</sub>=2, i.e., only the '''u''' and '''d''' quarks are treated as massless, the three [[pion]]s are the [[Goldstone boson]]s. When the '''s''' quark is also treated as massless, i.e., N<sub>f</sub>=3, all eight pseudoscalar [[meson]]s of the [[quark model]] become [[Goldstone boson]]s. The actual masses of these [[meson]]s are obtained in [[chiral perturbation theory]] through an expansion in the (small) actual masses of the quarks.
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| In other phases of [[quark matter]] the full chiral [[flavour (particle physics)|flavour]] symmetry may be recovered, or broken in completely different ways.
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| ===Evidence: experimental consequences===
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| The evidence for QCD condensates comes from two eras, the pre-QCD era 1950–1973 and the post-QCD era, after 1974. The pre-QCD results established that the strong interactions vacuum contains a quark chiral condensate, while the post-QCD results established that the vacuum also contains a gluon condensate.
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| ==== Pre-QCD: gradient coupling ====
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| In the 1950s, there were many attempts to produce a field theory to describe the interactions of [[pion]]s and nucleons. The obvious renormalizable interaction between the two objects is the [[Yukawa coupling]] to a pseudoscalar:
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| :<math>
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| L_I= \bar{N}\gamma_5 \pi N
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| \,</math>
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| And this is clearly theoretically correct, since it is leading order and it takes all the symmetries into account. But it doesn't match experiment. The interaction that does couples the nucleons to the ''gradient'' of the pion field.
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| :<math>
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| g \bar{N}\gamma^\mu \partial_\mu \pi N
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| \,</math>
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| This is the '''gradient-coupling model'''. This interaction has a very different dependence on the energy of the pion—it vanishes at zero momentum.
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|
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| This type of coupling means that a coherent state of low momentum pions barely interacts at all. This is a manifestation of an approximate symmetry, a '''shift symmetry''' of the pion field. The replacement
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| :<math>
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| \pi \rightarrow \pi+C
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| \,</math>
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| leaves the gradient coupling alone, but not the pseudoscalar coupling.
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| The modern explanation for the shift symmetry was first proposed by [[Yoichiro Nambu]]. The pion field is a [[Goldstone boson]], and the shift symmetry is the lowest order approximation to moving along the flat directions.
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| ==== Pre-QCD: Goldberger–Treiman relation ====
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| There is a mysterious relationship between the strong interaction coupling of the pions to the nucleons, the coefficient g in the gradient coupling model, and the axial vector current coefficient of the nucleon which determines the weak decay rate of the neutron. The relation is
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| :<math>
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| g_{\pi NN} F_\pi = G_A M_N
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| \,</math>
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| and it is obeyed to 10% accuracy.
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| The constant <math>G_A</math> is the coefficient that determines the neutron decay rate. It gives the normalization of the weak interaction matrix elements for the nucleon. On the other hand, the pion-nucleon coupling is a phenomenological constant describing the scattering of bound states of quarks and gluons.
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| The weak interactions are current-current interactions ultimately because they come from a nonabelian gauge theory. The Goldberger Treiman relation suggests that the pions for some reason interact as if they are related to the same symmetry current.
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| ===== PCAC =====
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| The phenomenon which gives rise to the Goldberger Treiman relation was called the "Partially Conserved Axial Current" hypothesis, or PCAC. Partially conserved is an archaic term for spontaneously broken, and the axial current is now called the chiral symmetry current.
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| The idea is that the symmetry current which performs axial rotations on the fundamental fields does not preserve the vacuum. This means that the current J applied to the vacuum produces particles. The particles must be scalars, otherwise the vacuum wouldn't be Lorentz invariant. By index matching, the matrix element is:
| |
| :<math>
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| J_\mu |0\rangle = k_\mu |\pi\rangle
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| \,,</math>
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| where <math>\! k_\mu</math> is the momentum carried by the created pion.
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| Since the divergence of the axial current operator is zero, we must have
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| :<math>
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| \partial_\mu J^\mu |0\rangle = k^\mu k_\mu |\pi\rangle = m_\pi^2|\pi\rangle = 0
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| \,.</math>
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| Hence the pions are massless, <math>m_\pi^2=0</math>, in accordance with [[Goldstone's theorem]].
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| Now if the scattering matrix element is considered, we have
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| :<math>
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| k_\mu \langle N(p) |\pi(k) N(p') \rangle = \langle N(p) | J_\mu |N(p')\rangle
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| \,.</math>
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| Up to a momentum factor, which is the gradient in the coupling, it takes the same form as the axial current turning a neutron into a proton in the current-current form of the weak interaction.
| |
| :<math> | |
| \langle N |J^\mu |N\rangle \langle e| J_\mu |\nu\rangle
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| \,</math>
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| ==== Pre-QCD: soft pion emission ====
| |
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| Extensions of the PCAC ideas allowed [[Steven Weinberg]] to calculate the amplitudes for collisions which emit low energy pions from the amplitude for the same process with no pions. The amplitudes are those given by acting with symmetry currents on the external particles of the collision.
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| These successes established the basic properties of the strong interaction vacuum well before QCD.
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| ====Pseudo-Goldstone bosons====
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| Experimentally it is seen that the masses of the [[Adjoint representation of a Lie group|octet]] of pseudoscalar mesons is very much lighter than the next lightest states; i.e., the octet of [[vector (geometric)|vector]] mesons (such as the [[rho]]). The most convincing evidence for SSB of the chiral [[flavour (particle physics)|flavour]] symmetry of QCD is the appearance of these [[pseudo-Goldstone boson]]s. These would have been strictly massless in the chiral limit. There is convincing demonstration that the observed masses are compatible with [[chiral perturbation theory]]. The internal consistency of this argument is further checked by [[lattice QCD]] computations which allow one to vary the quark mass and check that the variation of the pseudoscalar masses with the quark mass is as required by [[chiral perturbation theory]].
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| ====The η'====
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| This pattern of SSB solves one of the earlier "mysteries" of the [[quark model]], where all the pseudoscalar mesons should have been of nearly the same mass. Since ''N''<sub>f</sub> = 3, there should have been nine of these. However, one (the SU(3) singlet [[eta meson|η']]) has quite a larger mass than the SU(3) octet. In the quark model, this has no natural explanation— a mystery named the '''η−η' mass splitting''' (the η is one member of the octet, which should have been degenerate in mass with the η').
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| In QCD, one realizes that the η' is associated with the axial U(1) which is explicitly broken through the [[chiral anomaly]], and thus its mass is not "protected" to be small, like that of the η. (More technically, one says that [[instanton]]s generate the η-η' mass splitting.)
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| ====Current algebra and QCD sum rules====
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| PCAC and [[current algebra]] also provide evidence for this pattern of SSB. Direct estimates of the chiral condensate also come from such analysis.
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| Another method of analysis of [[correlation function (quantum field theory)|correlation function]]s in QCD is through an [[operator product expansion]] (OPE). This writes the [[vacuum expectation value]] of a non-local operator as a sum over VEVs of local operators, i.e., [[condensate (quantum field theory)|condensate]]s. The value of the correlation function then dictates the values of the condensates. Analysis of many separate correlation functions gives consistent results for several condensates, including the [[gluon condensate]], the [[quark condensate]], and many mixed and higher order condensates. In particular one obtains
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| ::<math>\langle (gG)^2\rangle\ \stackrel{\mathrm{def}}{=}\ \langle g^2 G_{\mu\nu}G^{\mu\nu}\rangle \simeq 0.5 {\rm\ GeV}^4</math>
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| ::<math>\langle \overline\psi\psi\rangle \simeq (-0.23)^3 {\rm\ GeV}^3</math>
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| ::<math>\langle (gG)^4\rangle\simeq 5:10\langle (gG)^2\rangle^2</math>
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| Here '''G''' refers to the [[gluon]] [[field (physics)|field]] [[tensor]], ψ to the [[quark]] [[field (physics)|field]], and g to the QCD coupling.
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| These analyses are being refined further through improved sum rule estimates and direct estimates in [[lattice QCD]]. They provide the ''raw data'' which must be explained by models of the QCD vacuum.
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| ==Models of the QCD vacuum== | |
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| A full solution of QCD would automatically give a full description of the vacuum, [[colour confinement|confinement]] and the [[hadron]] spectrum.{{Citation needed|date=August 2010}} [[Lattice QCD]] is making rapid progress towards providing the solution as a systematically improvable numerical computation. However, approximate models of the QCD vacuum remain useful in more restricted domains. The purpose of these models is to make quantitative sense of some set of condensates and [[hadron]] properties such as masses and [[form factor (quantum field theory)|form factor]]s.
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| This section is devoted to models. Opposed to these are systematically improvable computational procedures such as [[large N QCD]] and [[lattice QCD]], which are described in their own articles.
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| ===The Savvidy vacuum, instabilities and structure=== | |
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| This is a model of the QCD vacuum which at a basic level is a statement that it cannot be the conventional Fock vacuum empty of particles and fields. In 1977, [[George Savvidy]] showed<ref>{{Cite journal
| |
| | last = Savvidy | |
| | first = G. K.
| |
| | title = Infrared instability of the vacuum state of gauge theories and asymptotic freedom
| |
| | journal = Phys.Lett.
| |
| | volume = B | issue = 1
| |
| | page = 133
| |
| | year = 1977
| |
| | url = http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVN-471YRM4-39&_user=794998&_coverDate=11%2F07%2F1977&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000043466&_version=1&_urlVersion=0&_userid=794998&md5=f0ae24a24366968d858cfbabd07b3b1f
| |
| | doi = 10.1016/0370-2693(77)90759-6|bibcode = 1977PhLB...71..133S }}</ref> that the QCD vacuum with zero field strength is unstable, and decays into a state with a calculable non vanishing value of the field. Since [[condensate (quantum field theory)|condensate]]s are scalar, it seems like a good first approximation that the vacuum contains some non-zero but homogeneous field which gives rise to these condensates. This would then be a more complicated version of the [[Higgs mechanism]]. However, [[Stanley Mandelstam]] showed that a homogeneous vacuum field is also unstable. The instability of a homogeneous gluon field was argued by [[Niels Kjær Nielsen]] and [[Poul Olesen]] in their 1978 paper.<ref>{{Cite journal
| |
| | last1 = Nielsen | |
| | first1 = Niels Kjær
| |
| | last2 = Olesen
| |
| | first2 = Poul
| |
| | title = An unstable Yang–Mills field mode
| |
| | journal = Nucl.Phys.
| |
| | volume = B | issue = 144
| |
| | page = 376
| |
| | year = 1978
| |
| | url = http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVC-472T0MX-MX&_user=794998&_coverDate=11%2F13%2F1978&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000043466&_version=1&_urlVersion=0&_userid=794998&md5=ee1d1e4523eb4600826f5516514f9fb1
| |
| | doi = 10.1016/0550-3213(78)90377-2|bibcode = 1978NuPhB.144..376N }}</ref> These arguments suggest that the scalar condensates are an effective long-distance description of the vacuum, and at short distances, below the QCD scale, the vacuum may have structure.
| |
| | |
| ===The dual superconducting model=== | |
| | |
| In a type II [[superconductor]], [[electric charge]]s condense into [[Cooper pair]]s. As a result [[magnetic flux]] is squeezed into tubes. In the [[dual superconducting model|dual superconductor]] picture of the QCD vacuum, chromomagnetic monopoles condense into dual Cooper pairs, causing chromoelectric flux to be squeezed into tubes. As a result, [[colour confinement|confinement]] and the ''string picture'' of hadrons follows. This '''dual superconductor''' picture is due to [[Gerard 't Hooft]] and [[Stanley Mandelstam]]. [[Gerard 't Hooft|'t Hooft]] showed further that an [[Abelian projection]] of a non-Abelian [[gauge theory]] contains [[magnetic monopole]]s.
| |
| | |
| While the vortices in a type II superconductor are neatly arranged into a hexagonal or occasionally square lattice, as is reviewed in Olesen's 1980 seminar<ref>{{Cite journal
| |
| | last = Olesen | |
| | first = P.
| |
| | title = On the QCD vacuum
| |
| | journal = Phys.Scripta
| |
| | issue = 23
| |
| | page = 1000
| |
| | year = 1981
| |
| | url = http://iopscience.iop.org/1402-4896/23/5B/018/
| |
| | doi = 10.1088/0031-8949/23/5B/018
| |
| | volume = 23
| |
| |bibcode = 1981PhyS...23.1000O }}</ref> one may expect a much more complicated and possibly dynamical structure in QCD. For example, nonabelian [[Abrikosov vortex|Abrikosov-]][[Nielsen-Olesen vortex|Nielsen-Olesen vortices]] may vibrate wildly or be knotted.
| |
| | |
| ===String models===
| |
| | |
| String models of [[colour confinement|confinement]] and [[hadron]]s have a long history. They were first invented to explain certain aspects of [[crossing symmetry]] in the scattering of two [[meson]]s. They were also found to be useful in the description of certain properties of the [[Regge trajectory]] of the [[hadron]]s. These early developments took on a life of their own called the [[dual resonance model]] (later renamed [[string theory]]). However, even after the development of QCD string models continued to play a role in the physics of [[strong interaction]]s. These models are called ''non-fundamental strings'' or [[QCD string]]s, since they should be derived from QCD, as they are, in certain approximations such as the strong coupling limit of [[lattice QCD]].
| |
| | |
| The model states that the colour electric flux between a quark and an antiquark collapses into a string, rather than spreading out into a Coulomb field as the normal electric flux does. This string also obeys a different force law. It behaves as if the string had constant tension, so that separating out the ends (quarks) would give a potential energy increasing linearly with the separation. When the energy is higher than that of a meson, the string breaks and the two new ends become a quark-antiquark pair, thus describing the creation of a meson. Thus confinement is incorporated naturally into the model.
| |
| | |
| In the form of the [[Lund model]] Monte Carlo program, this picture has had remarkable success in explaining experimental data collected in electron-electron and hadron-hadron collisions.
| |
| | |
| ===Bag models===
| |
| | |
| Strictly, these models are not models of the QCD vacuum, but of physical single particle [[quantum states]] — the [[hadron]]s. The model proposed originally in 1974 by A. Chodos ''et al.'' <ref>Chodos, A., [[Robert Jaffe|Jaffe, R. L.]], Johnson, K., Thorn, C. B., [[Viki Weisskopf|Weisskopf, V. F.]] (1974). New extended model of hadrons, ''Phys. Rev. D9, 3471.'' {{doi|10.1103/PhysRevD.9.3471}}</ref>
| |
| consists of inserting a quark model in a ''perturbative vacuum'' inside a volume of space called a '''bag'''. Outside this bag is the real QCD vacuum, whose effect is taken into account through the difference between energy density of the true QCD vacuum and the perturbative vacuum (bag constant ''B'') and boundary conditions imposed on the quark [[wave function]]s and the gluon field. The [[hadron]] spectrum is obtained by solving the [[Dirac equation]] for quarks and the Yang–Mills equations for gluons.
| |
| The wave functions of the quarks satisfy the boundary conditions of a fermion in an infinitely deep potential well of scalar type with respect to the Lorentz group.
| |
| The boundary conditions for the gluon field are those of the dual color superconductor. The role of such a [[Dual superconductor model|superconductor]] is attributed to the physical vacuum of QCD. Bag models strictly prohibit the existence of open color (free quarks, free gluons, etc.) and lead in particular to string models of hadrons.
| |
| | |
| The '''chiral bag model''' couples the [[axial vector current]] <math>\overline\psi \gamma_5 \gamma_\mu\psi</math> of the quarks at the bag boundary to a [[pion|pionic field]] outside of the bag. In the most common formulation, the chiral bag model basically replaces the interior of the [[skyrmion]] with the bag of quarks. Very curiously, most physical properties of the nucleon become mostly insensitive to the bag radius. Prototypically, the [[baryon number]] of the chiral bag remains an integer, independent of bag radius: the exterior baryon number is identified with the topological [[winding number]] density of the Skyrme [[soliton]], while the interior baryon number consists of the valence quarks (totaling to one) plus the [[spectral asymmetry]] of the quark eigenstates in the bag. The spectral asymmetry is just the vacuum expectation value <math>\langle \overline\psi \gamma_0\psi\rangle</math> summed over all of the quark eigenstates in the bag. Other values, such as the total mass and the axial coupling constant <math>g_A</math>, are not precisely invariant like the baryon number, but are mostly insensitive to the bag radius, as long as the bag radius is kept below the nucleon diameter. Because the quarks are treated as free quarks inside the bag, the radius-independence in a sense validates the idea of [[asymptotic freedom]].
| |
| | |
| ===Instanton ensemble===
| |
| {{Main|instanton fluid}}
| |
| Another view states that [[BPST instanton|BPST]]-like [[instanton]]s play an important role in the vacuum structure of QCD. These instantons were discovered in 1975 by [[Alexander Belavin|Belavin]], [[Alexander Markovich Polyakov|Polyakov]], [[Albert S. Schwarz|Schwartz]] and [[Yu. S. Tyupkin|Tyupkin]]<ref>{{cite journal | last = Belavin | first = A.A. | coauthors = [[Alexander Markovich Polyakov|A.M. Polyakov]], A.S. Schwartz and Yu.S. Tyupkin | title = Pseudoparticle solutions of the Yang-Mills equations | journal = Phys. Lett. | volume = 59B | issue = 1 | pages = 85–87 | year = 1975 | url = http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVN-46YKS19-2PJ&_user=794998&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000043466&_version=1&_urlVersion=0&_userid=794998&md5=e69d57249fab742300bbb661acc70e8a | doi = 10.1016/0370-2693(75)90163-X |bibcode = 1975PhLB...59...85B }}</ref> as [[topology|topologically]] stable solutions to the Yang-Mills field equations. They represent [[quantum tunneling|tunneling]] transitions from one vacuum state to another. These instantons are indeed found in [[lattice QCD|lattice]] calculations. The first computations performed with instantons used the dilute gas approximation. The results obtained did not solve the infrared problem of QCD, making many physicists turn away from instanton physics. Later, though, an [[instanton fluid|instanton liquid model]] was proposed, turning out to be more promising an approach.<ref name="Hutter">{{cite arxiv| first = Marcus | last = Hutter | title = Instantons in QCD: Theory and application of the instanton liquid model | year = 1995 | eprint = hep-ph/0107098}}</ref>
| |
| | |
| The '''dilute instanton gas model''' departs from the supposition that the QCD vacuum consists of a gas of BPST-like instantons. Although only the solutions with one or few instantons (or anti-instantons) are known exactly, a dilute gas of instantons and anti-instantons can be approximated by considering a superposition of one-instanton solutions at great distances from one another. [[Gerard 't Hooft|'t Hooft]] calculated the effective action for such an ensemble,<ref>{{cite journal | last = 't Hooft | first = Gerard | authorlink = Gerardus 't Hooft | title = Computation of the quantum effects due to a four-dimensional pseudoparticle | journal = Phys. Rev. | volume = D14 | issue = 12 | pages = 3432–3450 | year = 1976 | doi = 10.1103/PhysRevD.14.3432 |bibcode = 1976PhRvD..14.3432T }}</ref> and he found an [[infrared divergence]] for big instantons, meaning that an infinite amount of infinitely big instantons would populate the vacuum.
| |
| | |
| Later, an '''[[instanton fluid|instanton liquid model]]''' was studied. This model starts from the assumption that an ensemble of instantons cannot be described by a mere sum of separate instantons. Various models have been proposed, introducing interactions between instantons or using variational methods (like the "valley approximation") endeavoring to approximate the exact multi-instanton solution as closely as possible. Many phenomenological successes have been reached.<ref name="Hutter"/> Whether an instanton liquid can explain confinement in 3+1 dimensional QCD is not known, but many physicists think that it is unlikely.
| |
| | |
| ===Center vortex picture===
| |
| A more recent picture of the QCD vacuum is one in which [[center vortex|center vortices]] play an important role. These vortices are [[topological defect]]s carrying a [[center (group theory)|center]] element as charge. These vortices are usually studied using [[lattice gauge theory|lattice simulations]], and it has been found that the behavior of the vortices is closely linked with the [[Color confinement|confinement]]-[[deconfinement]] phase transition: in the confining phase vortices percolate and fill the space-time volume, in the deconfining phase they are much suppressed.<ref>{{Cite journal | last1 = Engelhardt | first1 = M. | last2 = Langfeld | first2 = K. | last3 = Reinhardt | first3 = H. | last4 = Tennert | first4 = O. | title = Deconfinement in SU(2) Yang–Mills theory as a center vortex percolation transition | year = 2000 | journal = [[Physical Review D]] |volume=61 | issue = 5 | page = 054504 | doi = 10.1103/PhysRevD.61.054504|arxiv = hep-lat/9904004 |bibcode = 2000PhRvD..61e4504E }}</ref> Also it has been shown that the string tension vanished upon removal of center vortices from the simulations,<ref>{{Cite journal | last1 = Del Debbio | first1 = L. | last2 = Faber | first2 = M. | last3 = Greensite | first3 = J. | last4 = Olejník | first4 = Š. | title = Center dominance and ''Z''<sub>2</sub> vortices in SU(2) lattice gauge theory | year = 1997 | journal = [[Physical Review D]] | volume = 55 | issue = 4 | page = 2298 | doi = 10.1103/PhysRevD.55.2298|arxiv = hep-lat/9610005 |bibcode = 1997PhRvD..55.2298D }}</ref> hinting at an important role for center vortices.
| |
| | |
| ==See also==
| |
| * [[Vacuum state]] and [[vacuum#Quantum-mechanical definition|vacuum]]
| |
| * [[Spontaneous symmetry breaking]]
| |
| * [[Quantum chromodynamics]] and [[flavour (particle physics)|flavour]]
| |
| * [[Top quark condensate]]
| |
| * [[Goldstone boson]]
| |
| * [[Symmetry breaking]]
| |
| * [[Higgs mechanism]]
| |
| | |
| ==References and external links==
| |
| {{Reflist|2}}
| |
| | |
| ==Bibliography==
| |
| | |
| *''The quantum quark'', by Andrew Watson ISBN 0-521-82907-0
| |
| *''Handbook of QCD'', by M.A. Shifman ISBN 981-238-028-0
| |
| *''The QCD vacuum, hadrons and superdense matter'', by E.V. Shuryak ISBN 981-238-574-6
| |
| | |
| {{DEFAULTSORT:Qcd Vacuum}}
| |
| [[Category:Quark matter]]
| |
| [[Category:Vacuum]]
| |
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