Why do fermions strongly affect
the deconfinement?
Edward Shuryak
Stony Brook University
Based on unfinished paper with J.F.Liao
The outline
• Selfdual dyons vs monopoles: intro
• Monopoles in QGP: a reminder
• Deconfinement: Tc(Nf) and beta(Tc), three
regimes
• Fermionic zero modes (of monopoles); 2Nf
• Deconfinement in region one (Nf=0..4 or so)
• Deconfinement in region two (Nf=5..10 or so)
• Hints from N=2 Super-YM+matter
• Discussion
• Abeleization and topology
Magnetic objects and their
dynamics: classics
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Dirac explained how magnetic charges may coexists with quantum
mechanics (1934)
‘t Hooft and Polyakov discovered monopoles in Non-Abelian gauge
theories (1974)
‘t Hooft and Mandelstamm suggested “dual superconductor” mechanism
for confinement (1982)
Seiberg and Witten shown how it works, in the N=2 Super -Yang-Mills
theory (1994)
Two types of ``dyonic objects”
• Instantons => Nc selfdual dyons
(at nonzero holonomy <P>)
P van Baal
Those are the tunneling events at zero energy, E=iB =>E2+B2=0: Z is integral over
moduli spaces, good to discuss chiral symmetry breaking and fermion zero
modes
Instanton liquid
4d+short range
Dyonic plasma
3+1d long range
• (real time) excitations=> magnetic monopoles
Have nonzero energy and are physical excitations => Z is manybody integral over
paths, good to discuss confinement as their Bose-Einstein Condensation
• One can study both, are those studies dual to
each other? Unsal+Poppitz, May 2011 answer yes, for spatially
compactified N=2 SYM, but I will not discuss it
•
“magnetic scenario”:
(color)
magnetic monopoles
are important excitations
near Tc
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Four lectures on strongly coupled
Quark Gluon Plasma. Edward
Shuryak, (SUNY, Stony Brook) . 2009.
46pp. Published in
Nucl.Phys.Proc.Suppl.195:111156,2009.
Strongly coupled plasma with electric and magnetic charges.
Liao,ES, Phys.Rev.C75:054907,2007. hep-ph/0611131
Magnetic component of Yang-Mills plasma,M.N.Chernodub
and V.I.Zakharov, 98, 082002 (2007) [arXiv:hep-ph/0611228].
Electric Flux Tube in Magnetic Plasma. Liao,ES,
Phys.Rev.C77:064905,2008. arXiv:0706.4465
Magnetic monopoles in the high temperature phase of YangMills theories, A.D'Alessandro and M.D'Elia, Nucl.Phys.B 799,
241 (2008) [arXiv:0711.1266
Magnetic Component of Quark-Gluon Plasma is also a Liquid!
Liao,ES, Phys.Rev.Lett.101:162302,2008. e-Print:
arXiv:0804.0255
Angular Dependence of Jet Quenching Indicates Its Strong
Enhancement Near the QCD Phase Transition. Jinfeng Liao,,
Edward Shuryak Phys.Rev.Lett.102:202302,2009. e-Print:
arXiv:0810.4116
Thermal Monopole Condensation and Confinement in finite
``magnetic scenario”: Liao,ES hep-ph/0611131,Chernodub+Zakharov
Old good Dirac
condition
s(electric) s(magnetic)=1
=>electric/magnetic couplings (e/g)
must run in the opposite directions!
the “equilibrium line”
s(el)= s(mag) =1
needs to be in the
plasma phase
monopoles should be dense enough and
sufficiently weakly coupled before deconfinement
to get BEC
=>s(mag) < s(el): how small can s(mag)
be?
s(el)
s(mag)
The monopole density (vs T/Tc)
in confined and deconfined phases (Ratti,ES.08)
• The T=0 lattice point: from
Bornyakov,Ilgenfritz et al
• Near-Tc: condenced and
uncondenced monopoles, from
flux tubes (Liao ES)
• The solid line represent the
density of gluons suppresed by
<P>
g
m
• Note that the sum (g+mono) is
about const(T) except the peak
at Tc (the peak is not due to
dyons, as their density is flat)
Flux tubes do not disappear but get
higher tension around Tc
Large density
of uncondenced
monopoles
Vanishing density of condenced
monopoles
T
•4 jets (not 2) are produced in
each hard collisions
•Under proper conditions (high
density of monopoles) a moving
electric charge creates a flux tube
behind, with the tension up to 5
GeV/fm and not decaying
promtly
•Longitudinal tube is carried by
the radial flow in the direction
well correlated with the trigger
jet T (Shuryak 0706.3531, PRC76)
Our MD for 50-50 MQP/EQP
s(electric) and s(magnetic)
do run in opposite directions!
• Squares: fitted magnetic
coupling, circles: its inverse
compared to asymptotic
freedom (dashed)
• Effective plasma parameter
(here for magnetic)
• So, the monopoles are
never weakly coupled!
• (just enough to get Bosecondenced)
Bose-Einstein condensation of interacting particles
Bose-Einstein Condensation of strongly interacting bosons: From liquid He-4 to QCD
monopoles.Marco Cristoforetti , Edward Shuryak Phys.Rev. D80 (2009) 054013 e-Print:
arXiv:0906.2019)
• Feynman theory (for liquid He4): polygons
BEC if exp(-∆S(jump))>.16 or so (1/Nnaighbours)
• So there is a critical action Sc=1.65
• Feynman ignored the interaction
We calculated ``instantons” for particles
jumping paths in a liquid and
solid He4 incuding realistic atomic potentials
The superflow setting: a line of
particles move in one direction
Black straight line is Feynman’s
Noninteracting caloron
Red is our interacting one
Feynman’s criterion works for liquid
He4!
• The red point above is 1
atm He4
• Above right: solution
disapper for high
density, no supersolid
• Below right: reduction
of Tc with pressure is
qualitatively there
“supersolid” He4 ?
• ES+Cristoforetti: in solid it is always above the
Sc, so there is no supersolid He4 (because of a
bit higher density), but this is a play of
numbers (such as mass)
• This conclusion agrees with direct path
Monte-Carlo done before us… Experimentally
some disputes continue, moment of inertia at
T about 10-3K: some other bosonic
phenomena perhaps
The lesson: monopoles at Tc,
behave as He4 atoms =>Bose-Einstein
condensation
Deconfinement T(Nf) from the lattice
• Tc decreases with Nf (<= in units such that T=0 confining string
tension = const), it is 270 MeV at Nf=0, about 170 at real QCD Nf=2.5 etc
• I prefer to use the absolute coupling instead
(evolved from beta(1/a)=>beta(Tc) according to Nt
In 2-loop approximation)
• The three regions
The black line
Is the twoloop zero of
the beta
function:
Conformal
window
I
II
III
Nf
Fermionic zero modes of the
monopoles
• Starting in the simplest Nc = 2 theory we use the
term “isospin” instead of the color. Thus the
fundamental (adjoint) quarks have isospin T=1/2
(1), respectively.
• grandspin K = T + S takes values 1/2 + 1/2 = 0, 1
and 1 + 1/2 = 1/2, 3/2
• From the number of zero modes, 1 and 2
respectively, one can see that zero modes
correspond to K = 0 and K = 1/2 in those two
cases.
Fermionic zero mode, contd
• path integral with one complex coefficient => in
the operator language, a pair of
creation/annihilation operators with the algebra
[aa+] = 1 requiring representation in the form of
two states, the “empty” and “occupied” ones.
• Exponential proliferation of states 2Nf !
• (for those in doubts, a homework: calculate quantum number
and multiplicity of magnetic states in N=4,Nf=0 SYM, as well
as N=2, Nf=4. You should find that both are E/M selfdual =>
thus conformal! No need to calculate loops…)
Qualitative picture of BEC, in region 1
Rounds are
“empty”
monopoles,
they are
identical and
can make BEC
“polygons”
Other shapes have
q’s and thus
flavors, they are
distinquishable
Deconfinement in the region I
• The fraction of the monopoles without quarks
F(empty)=1/2Nf decreases, but it still can be
compensated by going to stronger coupling and
decreasing their (magnetic) coupling
• Using Feynman criterium for BEC, Sc=const
(relativistic form!) one can get the effect
• As monopoles are not static and modes are not exactly zero, we
introduced some penalty per quark + repulsion between quarks
Qualitative picture in the region II
for superflow setting
q
M
• Practically all monopoles have quarks
• But they still can make a supercurrent, provided the
Feynman criterium is satisfied!
discussion
• Are there different confinements?
• e.g. BEC of monopoles in 3+1 versus vortices in
2+1. So what happens when 1dim is
compactified? (Cossu, D’Elia arXiv:0904.1353,
Na=2 => two confining phases found, but they
are separated by 2 deconfined ones, and we do
not know if they can be continuously(?))
• Or BEC of the QM=2 vs QM=1 objects in
N=2,
Nf=3 SYM: can one find each of them and find out
which is BE-Condenced?
Adjoint quarks and hints from SUSY
• Example 1: Na=1,Nf=4 => like N=2, Nf=4 SYM
which is fully conformal. (The difference is only in
scalars, so it is near-conformal; but if one starts
from magnetic formulation, how these scalars
not to appear?)
• Example 2: Na=1,Nf=3 => like N=2, Nf=3 SYM for
which SW found two vacua: one 4-degenerate
has confinement and chiral symm.breaking,
another 1-degenerate has only confinement with
an unusual magnetic charge QM=2
“Abeleization” and topology
• Higgsing assumed, <A0>, separate 8 SU(3)
gluons into 6 massive and 2 massless:
• Magnetic plasma => dual MHD (ES,2009) in
QGP corona
• Long-range 2 U(1)’s lead to flux tubes which
remain very robust, till about T=1.4Tc (Liao,ES)
Instantons as un-knotting of the flux
tubes (Kharzeev,ES)
• Chern-Simons #: F^A+A^A^A=Abelian+non-Ab.
terms. The su(2) instantons-sphalerons use the
latter term for mapping
• The former term actually has meaning in
electrodynamic plasmas, indicating knottingness
of the flux tubes
• Knots are present in the lab and solar plasmas,
their decay events are currently studied, by
solving MHD eqns
• Even we found a proposal that the ball lightning is
a magnetic knot
The time history; note a jump
corresponding to un-knotting
(we call the sphaleron transition)
Abelian magnetic knots
summary
• Are there different confinements?
• Fermions ride on monopoles and make BEC
difficult => deconfinement at stronger
coupling => penetrate deeper into the
magnetic-dominance region
• Same magnetic states in SYM and special
ordinary QCD-like theories => can any
similarity be found?
• “Abeleization” does not wipe out topology!
extras
Two potentials - two tensions
Large density
of uncondenced
monopoles
Vanishing density of condenced
monopoles
Simic+Unsal
• Quantum problem of gluon-monopole scattering
• n=eg is the only parameter, if we ignore the monopole
core and keep only Coulomb B field
j’ is not an integer!
C.Ratti+ES, large correction to transport properties from
the (large angle) gluon-monopole scatterng
• RHIC: T/Tc<2, LHC T/Tc<4: we predict hydro will
still be there, with h/s about .2