Magnetic monopoles in lattice QCD Results Open problems Summary Magnetic monopoles in high temperature QCD Nucl. Phys. B 799 (2008), 241 � 2 , M. D’Elia 1 A. D’Alessandro 1 1 Università di Genova & INFN 2 Speaker at the conference GGI workshop, Florence A. D’Alessandro, M. D’Elia Nucl. Phys. B 799 (2008), 241 (arXiv:0711.1266)
Magnetic monopoles in lattice QCD Results Open problems Summary Outline Magnetic monopoles in lattice QCD 1 Results 2 Monopole-(anti)monopole correlation function Monopole density Open problems 3 The gauge dependence problem The Gribov ambiguity A. D’Alessandro, M. D’Elia Nucl. Phys. B 799 (2008), 241 (arXiv:0711.1266)
✄ Magnetic monopoles in lattice QCD Results Open problems Summary Motivation Abelian magnetic monopoles are candidates for explaining color confinement within the dual superconducting model of the QCD vacuum (confinement is induced by the breaking of a ✁ 1 magnetic U ✂ symmetry via monopole condensation). The magnetic component is supposed to be relevant ( Chernodub & Zakharov ’06, Liao & Shuryak ’06 in explaining the physical properties of the Quark Gluon Plasma phase (above the transition). It has been identified ( Chernodub & Zakharov ’06 ) with abelian magnetic monopoles “evaporating” from the condensate at T T c . A. D’Alessandro, M. D’Elia Nucl. Phys. B 799 (2008), 241 (arXiv:0711.1266)
☞ ✞ ✞ ✍ Magnetic monopoles in lattice QCD Results Open problems Summary The Abelian Projection How can we get abelian monopoles from a non abelian theory such as QCD? ✁ 1 First we fix a gauge that leaves a U ✂ residual symmetry: in the Maximal Abelian Gauge we maximize ✁ x ✁ x � x Re tr F MAG ✠ U ✂☛✡ 3 U ✂✌✡ 3 ☎✝✆✟✞ Then we take the diagonal part of the links (Abelian Projection) Possible dependence of the abelian observables on the gauge fixed prior the projection!!! A. D’Alessandro, M. D’Elia Nucl. Phys. B 799 (2008), 241 (arXiv:0711.1266)
☞ ✞ ✞ ✍ Magnetic monopoles in lattice QCD Results Open problems Summary The Abelian Projection How can we get abelian monopoles from a non abelian theory such as QCD? ✁ 1 First we fix a gauge that leaves a U ✂ residual symmetry: in the Maximal Abelian Gauge we maximize ✁ x ✁ x � x Re tr F MAG ✠ U ✂☛✡ 3 U ✂✌✡ 3 ☎✝✆✟✞ Then we take the diagonal part of the links (Abelian Projection) Possible dependence of the abelian observables on the gauge fixed prior the projection!!! A. D’Alessandro, M. D’Elia Nucl. Phys. B 799 (2008), 241 (arXiv:0711.1266)
☞ ✞ ✞ ✍ Magnetic monopoles in lattice QCD Results Open problems Summary The Abelian Projection How can we get abelian monopoles from a non abelian theory such as QCD? ✁ 1 First we fix a gauge that leaves a U ✂ residual symmetry: in the Maximal Abelian Gauge we maximize ✁ x ✁ x � x Re tr F MAG ✠ U ✂☛✡ 3 U ✂✌✡ 3 ☎✝✆✟✞ Then we take the diagonal part of the links (Abelian Projection) Possible dependence of the abelian observables on the gauge fixed prior the projection!!! A. D’Alessandro, M. D’Elia Nucl. Phys. B 799 (2008), 241 (arXiv:0711.1266)
☞ ✞ ✞ ✍ Magnetic monopoles in lattice QCD Results Open problems Summary The Abelian Projection How can we get abelian monopoles from a non abelian theory such as QCD? ✁ 1 First we fix a gauge that leaves a U ✂ residual symmetry: in the Maximal Abelian Gauge we maximize ✁ x ✁ x � x Re tr F MAG ✠ U ✂☛✡ 3 U ✂✌✡ 3 ☎✝✆✟✞ Then we take the diagonal part of the links (Abelian Projection) Possible dependence of the abelian observables on the gauge fixed prior the projection!!! A. D’Alessandro, M. D’Elia Nucl. Phys. B 799 (2008), 241 (arXiv:0711.1266)
✚ ✞ ✒ ✚ ✞ ☎ ✘ ☎ Magnetic monopoles in lattice QCD Results Open problems Summary De Grand-Toussaint On abelian projected configurations monopole currents are defined as 1 m ✞✓✒✕✔✗✖✙✘ ✛✜✔✗✖ 2 ✎✑✏ where ✛✜✔✗✖ is the compactified part of the abelian plaquette phase ( De Grand & Toussaint ’80 ). De Grand elementary cube (in 3D) Quantization of charge Closure of monopole currents: ✞ m 0 A. D’Alessandro, M. D’Elia Nucl. Phys. B 799 (2008), 241 (arXiv:0711.1266)
✢ ✣ ✄ ✧ ✂ Magnetic monopoles in lattice QCD Results Open problems Summary The thermal monopole density At T T c magnetic currents are virtual; At T T c currents and monopoles become real (magnetic currents percolate in temporal direction). Real particle = wrapped trajectory on the compact t direction ( Chernodub & Zakharov ’07 ). � t ✧ N wrap ★ m 0 ★✪✩ x ✫✬✫ ✤✦✥ x = V s ✁✮✭ x m 0 ✯ t = magnetic trajectory in time direction A. D’Alessandro, M. D’Elia Nucl. Phys. B 799 (2008), 241 (arXiv:0711.1266)
✢ ✣ ✄ ✧ ✂ Magnetic monopoles in lattice QCD Results Open problems Summary The thermal monopole density At T T c magnetic currents are virtual; At T T c currents and monopoles become real (magnetic currents percolate in temporal direction). Real particle = wrapped trajectory on the compact t direction ( Chernodub & Zakharov ’07 ). � t ✧ N wrap ★ m 0 ★✪✩ x ✫✬✫ ✤✦✥ x = V s ✁✮✭ x m 0 ✯ t = magnetic trajectory in time direction A. D’Alessandro, M. D’Elia Nucl. Phys. B 799 (2008), 241 (arXiv:0711.1266)
✢ ✣ ✄ ✧ ✂ Magnetic monopoles in lattice QCD Results Open problems Summary The thermal monopole density At T T c magnetic currents are virtual; At T T c currents and monopoles become real (magnetic currents percolate in temporal direction). Real particle = wrapped trajectory on the compact t direction ( Chernodub & Zakharov ’07 ). � t ✧ N wrap ★ m 0 ★✪✩ x ✫✬✫ ✤✦✥ x = V s ✁✮✭ x m 0 ✯ t = magnetic trajectory in time direction A. D’Alessandro, M. D’Elia Nucl. Phys. B 799 (2008), 241 (arXiv:0711.1266)
✢ ✣ ✄ ✧ ✂ Magnetic monopoles in lattice QCD Results Open problems Summary The thermal monopole density At T T c magnetic currents are virtual; At T T c currents and monopoles become real (magnetic currents percolate in temporal direction). Real particle = wrapped trajectory on the compact t direction ( Chernodub & Zakharov ’07 ). � t ✧ N wrap ★ m 0 ★✪✩ x ✫✬✫ ✤✦✥ x = V s ✁✮✭ x m 0 ✯ t = magnetic trajectory in time direction A. D’Alessandro, M. D’Elia Nucl. Phys. B 799 (2008), 241 (arXiv:0711.1266)
✔ ✔ ✂ ✰ ✳ ✱ ✱ ✔ ✰ ✱ ✔ ✰ ✰ ✔ ✰ ✫ ✴ ✔ ✰ ✱ ✂ ✂ ☎ ✻ ✂ ☎ ✫ Magnetic monopoles in lattice QCD Results Open problems Summary The monopole-(anti)monopole correlation function ✁ r ★ 0 ★ r ✫✲✱ g = (monopole-monopole) ✁ r ✔✗✳ ★ 0 ✔✵✴ ★ r ✫✶✱ g = (monopole-antimonopole) 1 g ✷ r ✸✺✹ g(r)-free gas g(r)-liquid g(r)-solid ✁ r 1 no interaction g ✁ r If the interaction potential V ✂ is weak we can extract it ✁ r ✁✽✼ V ✁ r through g ✂ . exp ✂✿✾ T A. D’Alessandro, M. D’Elia Nucl. Phys. B 799 (2008), 241 (arXiv:0711.1266)
✔ ✔ ✂ ✰ ✳ ✱ ✱ ✔ ✰ ✱ ✔ ✰ ✰ ✔ ✰ ✫ ✴ ✔ ✰ ✱ ✂ ✂ ☎ ✻ ✂ ☎ ✫ Magnetic monopoles in lattice QCD Results Open problems Summary The monopole-(anti)monopole correlation function ✁ r ★ 0 ★ r ✫✲✱ g = (monopole-monopole) ✁ r ✔✗✳ ★ 0 ✔✵✴ ★ r ✫✶✱ g = (monopole-antimonopole) 1 g ✷ r ✸✺✹ g(r)-free gas g(r)-liquid g(r)-solid ✁ r 1 no interaction g ✁ r If the interaction potential V ✂ is weak we can extract it ✁ r ✁✽✼ V ✁ r through g ✂ . exp ✂✿✾ T A. D’Alessandro, M. D’Elia Nucl. Phys. B 799 (2008), 241 (arXiv:0711.1266)
✔ ✔ ✂ ✰ ✳ ✱ ✱ ✔ ✰ ✱ ✔ ✰ ✰ ✔ ✰ ✫ ✴ ✔ ✰ ✱ ✂ ✂ ☎ ✻ ✂ ☎ ✫ Magnetic monopoles in lattice QCD Results Open problems Summary The monopole-(anti)monopole correlation function ✁ r ★ 0 ★ r ✫✲✱ g = (monopole-monopole) ✁ r ✔✗✳ ★ 0 ✔✵✴ ★ r ✫✶✱ g = (monopole-antimonopole) 1 g ✷ r ✸✺✹ g(r)-free gas g(r)-liquid g(r)-solid ✁ r 1 no interaction g ✁ r If the interaction potential V ✂ is weak we can extract it ✁ r ✁✽✼ V ✁ r through g ✂ . exp ✂✿✾ T A. D’Alessandro, M. D’Elia Nucl. Phys. B 799 (2008), 241 (arXiv:0711.1266)
✴ ● Magnetic monopoles in lattice QCD Results Monopole-(anti)monopole correlation function Open problems Monopole density Summary Monopole-(anti)monopole correlation function I 1.2 g(r) 0.8 T/Tc = 1.10 T/Tc = 1.19 T/Tc = 1.42 T/Tc = 1.63 0.4 T/Tc = 3.80 0.2 0.4 0.6 0.8 r [fm] Fit with screened Coulomb V ❄❆❅✵❇ r , ❋ 2 fm ; r ★ r M e 0 ✫❁❀❃❂ ❈❊❉ Liquid-like structure!! Stronger M coupling at high T ( Liao & Shuryak ’07 ); Agreement with MD simulation of std. EM plasma ( Liao & Shuryak ’07 ). A. D’Alessandro, M. D’Elia Nucl. Phys. B 799 (2008), 241 (arXiv:0711.1266)
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