Strong Magnetic Fields in QCD Lattice Calculations

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Strong Magnetic Fields in QCD Lattice
Calculations

• P.V.Buividovich (ITEP, JINR)?,
• M.N.Chernodub (LMPT, Tours University, ITEP)?,
• E.V.Luschevskaya (ITEP, JINR)?,
• M.I.Polikarpov (ITEP)?

NICA Roundtable Workshop IV
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Some slides are made by M.N. Chernodub, P.V.
Buividovich and by D.E. Kharzeev
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Overview

• n Lattice simulations with magnetic fields
• n Chiral symmetry breaking Dirac eigenmodes and
  their localization
• n Magnetization of the vacuum first lattice
  results
• n Chiral Magnetic Effect
• n Quark electric dipole moment

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Magnetic fields in non-central collisions
The medium is filled with electrically charged
particles Large orbital momentum, perpendicular
to the reaction plane Large magnetic field along
the direction of the orbital momentum
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We calculate
in the external magnetic field and in
the presence of the vacuum gluon fields
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2
1
0
T
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We consider SU(2) gauge fields and quenching
approximation
3
2
1
0
T
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Effects observed at very strong magnetic fields
on the lattice

• 1. Enhancement of the chiral condensate(arXiv081
  2.1740) talk of E.V. Luschevskaya
• 2. Magnetization of the QCD vacuum(arXiv0906.048
  8)
• 3. Chiral Magnetic Effect (arXiv0907.0494)
  talk of P.V. Buividovich
• 4. We observe very large correlation between
  quark electric dipole moment and chirality (not
  yet published)

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Chiral condensate vs. field strength
We are in agreement with the chiral perturbation
theory the chiral condensate is a linear
function of the strength of the magnetic field!
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Magnetic susceptibility - results
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Chiral Magnetic Effect
Fukushima, Kharzeev, Warringa, McLerran 07-08
Electric current appears at regions 1. with
non-zero topological charge density 2. exposed
to external magnetic field
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Chiral Magnetic Effect on the lattice,
qualitative picture
Density of the electric charge vs. magnetic field
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Chiral Magnetic Effect on the lattice,
qualitative picture
Non-zero field, subsequent time slices
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Chiral Magnetic Effect on the lattice,
qualitative picture
Effect of field increasing
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Magnetic fields in non-central collisions
The medium is filled with electrically charged
particles Large orbital momentum, perpendicular
to the reaction plane Large magnetic field along
the direction of the orbital momentum
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Magnetic fields in non-central collisions
Instanton
The medium is filled with electrically charged
particles Large orbital momentum, perpendicular
to the reaction plane Large magnetic field along
the direction of the orbital momentum
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Chiral Magnetic Effect on the lattice, RESULTS
and QUESTIONS
D. Leinweber Topological charge density after
vacuum cooling
S.Morozov, F.Gubarev, M.Polikarpov, V.
Zakharov Density of eigenfunctions of the
Dirac equation in not cooled vacuum
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Electric dipole moment of quark
yLarge correlation between square of the
electric dipole moment
and chirality
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Effects observed at very strong magnetic fields
on the lattice

• 1. Enhancement of the chiral condensate(arXiv081
  2.1740) talk of E.V. Luschevskaya
• 2. Magnetization of the QCD vacuum(arXiv0906.048
  8)
• 3. Chiral Magnetic Effect (arXiv0907.0494)
  talk of P.V. Buividovich
• 4. We observe very large correlation between
  quark electric dipole moment and chirality (not
  yet published)

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Our plans

• 1. SU(2) -gt SU(3) (in progress)
• 2. Finite chemical potential m (in progress)
• 3. Dynamical quarks (fermionic determinant sign
  problem at finite magnetic field)