deconfinement Edward Shuryak Stony Brook University Based on unfinished paper with JFLiao The outline Selfdual dyons vs monopoles intro Monopoles in QGP a reminder Deconfinement ID: 245679
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Slide1
Why do fermions strongly affect the deconfinement?
Edward ShuryakStony Brook University
Based on unfinished paper with
J.F.LiaoSlide2
The outline
Selfdual dyons vs
monopoles: intro
Monopoles in QGP: a reminder
Deconfinement
:
T
c
(N
f
) and
beta(Tc
), three regimes
Fermionic
zero modes (of monopoles); 2
Nf
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 topologySlide3
Magnetic objects and their dynamics: classics
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)Slide4
Two types of ``dyonic objects”
Instantons =>
N
c
selfdual
dyons (at nonzero holonomy <P>)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(real time) excitations=>
magnetic monopolesHave 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
Instanton liquid4d+short range
Dyonic plasma3+1d long range
P van BaalSlide5
“magnetic scenario”: (color)
magnetic monopolesare important excitations near Tc
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:0706.4465Magnetic monopoles in the high temperature phase of Yang-Mills 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:0810.4116Thermal Monopole Condensation and Confinement in finite temperature Yang-Mills Theories. Alessio
D'Alessandro, Massimo D'Elia, Edward Shuryak, . Feb 2010. PRD.
Four lectures on strongly coupled Quark Gluon Plasma. Edward Shuryak, (SUNY, Stony Brook) . 2009. 46pp. Published in Nucl.Phys.Proc.Suppl.195:111-156,2009.Slide6
=>electric/magnetic couplings (e/g)
must run in the opposite directions!
Old good Dirac condition
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
(electric)
s
(magnetic)=1
``magnetic scenario”:
Liao,ES hep-ph/0611131,Chernodub+Zakharov
s
(el)
s
(mag)Slide7
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>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)
g
mSlide8
Flux tubes do not disappear but get higher tension around Tc
Large density
of
uncondenced
monopoles
Vanishing density of
condenced
monopolesSlide9
There are evidences for these flux tubes in the “QGP corona” known as “hard ridge”
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)
TSlide10
Our MD for 50-50 MQP/EQPSlide11
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 Bose-condenced)Slide12
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/N
naighbours)So there is a critical action Sc=1.65Feynman ignored the interaction
We calculated ``
instantons
” for particles jumping paths in
a liquid and
solid He4 incuding
realistic atomic potentialsSlide13
The superflow setting: a line of particles move in one direction
Black straight line is Feynman’s
Noninteracting
caloron
Red is our interacting oneSlide14
Feynman’s criterion works for liquid He4!
The red point above is 1
atm
He4
Above right: solution
disapper
for high density, no supersolidBelow right: reduction of Tc
with pressure is qualitatively there Slide15
“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 perhapsSlide16
The lesson: monopoles at
T
c
,
behave as
He
4
atoms
=>Bose-Einstein condensationSlide17
Deconfinement T(N
f) from the lattice
Tc
decreases with
N
f
(<= 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 NtIn 2-loop approximation)
The three regions
I
II
III
N
f
The black line
Is the two-loop zero of the beta
f
unction:
Conformal
windowSlide18
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, 3/2From 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. Slide19
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, N
f=4. You should find that both are E/M selfdual
=> thus conformal! No need to calculate loops…)Slide20
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
distinquishableSlide21
Deconfinement in the region I
The fraction of the monopoles without quarks
F(empty
)=1/2
N
f decreases, but it still can be
compensated by going to stronger coupling anddecreasing 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 quarksSlide22
Qualitative picture in the region IIfor superflow
setting
Practically all monopoles have quarks
But they still can make a
supercurrent
, provided the Feynman
criterium is satisfied!
M
qSlide23
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? Slide24
Adjoint quarks and hints from SUSY
Example 1: Na=1,N
f
=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,N
f=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 Q
M=2Slide25
“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)Slide26
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 mappingThe former term actually has meaning in
electrodynamic plasmas, indicating knottingness of the flux tubesKnots are present in the lab and solar plasmas, their decay events are currently studied, by solving MHD
eqnsEven we found a proposal that the ball lightning is a magnetic knot Slide27
The time history; note a jump corresponding to un-knotting
(we call the sphaleron transition)Slide28
Abelian magnetic knotsSlide29
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!Slide30
extrasSlide31
Two potentials - two tensions
Large density
of
uncondenced
monopoles
Vanishing density of
condenced
monopolesSlide32
Simic+UnsalSlide33
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!Slide34
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