QCD on : from confinement/deconfinement to the effect of ...
Transcript of QCD on : from confinement/deconfinement to the effect of ...
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M O H A M E D A N B E R
I N S T I T U T E O F T H E O R E T I C A L P H Y S I C S
R E C E N T D E V E L O P M E N T S I N S E M I C L A S S I C A LP R O B E S O F Q U A N T U M F I E L D T H E O R I E S
A C F I , U M A S S A M H E R S T
M A R C H 1 9 , 2 0 1 6
QCD(adj) on :Confinement/Deconfinement Transitions
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13 SR
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Preliminaries
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Deconfinement transitions
Weak coupling Strong coupling
Study analytically Lattice simulations
Link?
compare
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Preliminaries
Confinement is the mechanism for holding quarks inside nucleons: no isolated color charges
This picture has been confirmed through extended lattice simulations
RV
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Not confined
Confined
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Quark-Antiquark + -
Charges in QED
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Preliminaries
As we increase the temperature deconfinementphase transition
Quark-gluon plasma: a new state of matter
We need an order parameter
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cTT + - + -
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Preliminaries
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Watch out! Many circles!
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Preliminaries
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Order parameter in pure YM: Polyakov loop
is gauge invariant
transforms under the center
s
dxAi
FFF pe00
trtrP
Thermal circle: compact time ncecircumfere
11
T
FP
txAtxA ,,
2222)2(FF , Z,PP IIz SU
FP
S
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Preliminaries
Confined phase: the center is preserved
Deconfined phase: the center is broken
The physics is that
cTT 0, FP
cTT 0, FP
TF
F eP /~
FP
cT 0
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Free energy of quarks
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Preliminaries
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Pure YM is very difficult since the transition happens at QCD
Nonabelianconfinement
Deconfinement
0exptr][tr 00FFF
s
dxAiP
Increase T
0][trF
QCDcT ~cTT
Eigenvaluedistribution
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Preliminaries
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Pure YM is strongly coupled, we can not do semi-classical analysis
Brute force calculations gives
This potential is minimized when , so center symmetry is broken
True for
)(1tr21 2
1
2
442gO
nV
n
n
per
Ntr
QCDT
Deconfinement
QCDcT ~
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Preliminaries
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This potential can not capture the phase transition
The hope is that a non-perturbative part can help:
But pure YM is strongly coupled at the transition and no reliable semi-classics can help
pernon
g
a
per VeVgV
22
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Preliminaries
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Analytic understanding: separation of scale
This is QCD(adj) on
3A
0][tr
1311,2 SRSR
),,,(),,,(
),,,(),,,(
Lztyxztyx
LztyxAztyxA
Periodic boundary conditions
Adjoint fermions
)4(SU
1S L
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Preliminaries
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Motivation:
Hosotani Mechanism (unification)
Egushi-Kawai reduction (Large-N volume independence, dream!)
Laboratory for gauge theories
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Preliminaries
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Progress: (see M. Unsal and T. Sulejmanpasic talks)
Confinement in QCD(adj) (microscopic picture)M. Unsal 2009; M. Unsal, E Poppitz 2010, M.A, E. Poppitz 2011; T Misumi, M. Nitta, N.
Sakai 2014; T Misumi, T. Kanazawa 2014
Deconfinement transition in hot QCD(adj)M. A, E. Poppitz, M. Unsal 2012; M. A, S. Collier, E. Poppitz 2013; M. A, S. Collier, S.
Strimas-Mackey, E. Poppitz, B, Teeple 2013
Deconfinement in pure YM through a continuity conjecture YM QCD(adj)E. Poppitz, T. Schafer, M. Unsal 2012; E. Poppitz, T.Schafer, M. Unsal 2013; E. Poppitz,
T Sulejmanpasic 2013; M.A. 2013; M.A.; M.A., B. Teeple, E. Poppitz 2014
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Preliminaries
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Resurgence and the renormalon problem in QCD(adj)M. Unsal, P. Argyres 2012; M. A., T. Sulejmanpasic 2014
Strings in QCD(adj)M.A., E. Poppitz, T. Sulejmanpasic 2015
Global structure in QCD(adj)M.A., E. Poppitz 2015
Lattice QCD(susy)G. Bergner, S. Piemonte 2014, G. Bergner, G. Giudice, G. Munster, S. Piemonte 2015
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Preliminaries
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Goals of studying the theory on a circle
Analytic understanding of the physics
Compare the results on the circle with lattice results on
The ultimate goal is to decompactify the theory (Clay Mathematics Institute $1000,000 question!!)
4R
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Outline
Part I: Confinement in QCD(adj) on
Part II: Deconfinement in pure YM on
Part III: Deconfinement in hot QCD(adj) on
13 SR
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13 SR
4R
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Part I:
Formulation and confinement
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QCD(adj) on : Formulation
model Glashow-Georgi
3
22
32
small
2
)(22
1-tr
2i2
1-tr
1
3
13
AVg
ADFFg
L
DFFg
S
peri
R
L
Im
m
I
mn
mn
SR
Compact scalar One-loop effect
Adjoint fermions with periodic boundary conditions along the circle5.51 fn 1S
13 SR
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:)2(SU
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QCD(adj) on : Formulation
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One-loop calculation
For center symmetry is preserved;
At we find . This is SUSY. The center is stabilized by non-perturbative effects
13 SR
33
1
2
442tr
21
dxAi
n
nf
per
e
nL
nV
1fn 0perV
SU(2)
1fn
1fn
1N
0tr
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QCD(adj) on : Formulation
Higsing: the theory abelianizes
At small the gauge coupling freezes at a small value
In 3D the photon has one degree of freedom
QCDL /1
)1()2( USU
2
FF
13 SR
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LMW
1~
)2(SU
QCD
)1(U
)(Eg
EL/1
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QCD(adj) on : Formulation
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For
For (SUSY), the field is massless (modulus)
13 SR
1fn
1fn 3A
,22
IIeff i LA3
,2
IIeff i
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QCD(adj) on : Formulation
More interesting story to tell: non-perturbativeeffects
Feynman path integral
paths
EuclideanES
eZ
Perturbative +non-perturbative (instantons)
Instantons
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QCD(adj) on : Formulation
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Magnetic bion Neutral bion
13 SR
2 M. Unsal 2009
2
82
2
ee g
2
82
2
ig ee
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QCD(adj) on : Formulation
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Summing up all contributions:
For
For SUSY
2cosh 2cos 00
massphoton
22
bosoniceff
SSee
13 SR
Notice the relative sign, from analytic continuation
1fn
2
2
0
massphoton
2
bosoniceff
8 , 2cos0
gSe
S
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QCD(adj) on : Confinement
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Magnetic bions proliferate in the vacuum: 3D Coulomb gas
13 SR
3/0SLe
2
2
2
2
2
2
2
2
2
2
22
22
2rg 2
1
Electric charge Electric charge+ -
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SUSY on : Confinement
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One can use chiral dualities to dualize the photon
Perturbatively:
Next we add the nonperturbative part:
iX
XXKxddS ),(43
)( 23
pert-non XWXWxddS
2
28
~ gX
X eeW
13 SR
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SUSY on : Confinement
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Then one obtains:
13 SR
2cosh2cos
2cosh2cos~
0
0
22
4
S
S
e
AeX
W
X
WV
Magnetic and neutral bions are the physical manifestation
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QCD(adj) on : Confinement
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Take home messages
QCD(adj) preserves the center separation of scales
QCD(adj) trivial perturbatively
Confinement is due to magnetic bions
SUSY is curse and blessing!
13 SR
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Part II: Phase Transition in pure YM on via mass deformed SUSY
on 13 SR
4R
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Mass deformed SUSY on
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Adding mass deformation (MD) to Super-Yang-Mills
(QCD(adj) with ), we can study phase transition in pure Yang-Mills
13 SR
1fn
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Mass deformed SUSY on
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13 SR
T. Schafer, E. Poppitz, M. Unsal 2012
?
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Mass Deformed SUSY on
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Now, we add a massive fermion (gaugino)
The mass lifts the fermions zero mode
Monopoles contribute to the potential
13 SR
coshcos~2
2/0
L
meV
S
m
2cosh2cos
c.c.
00
0 2/22
SS
m
i
m
iS
eff
ee
eee
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Mass deformed SUSY on
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Total potential
stabilizes the center
destabilizes the center
The competition between and determines the nature of the quantum phase transition
13 SR
mbion V
g
V
g
t eL
me
LV
coshcos2cosh2cos1 2
2
2
2 4
2
8
3
bionV
mV
bionV mV
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Phase transitions in pure YM
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Behavior of the Polyakov loop
0][tr 0][tr
.
][tri
e
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Phase transitions in pure YM
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The phase transition is first order in all groups:
SU(N), spin(2N+1), Sp(2N), Spin(2N),
E6, E7,E8,F4,G2. M.A, B. Teeple, E. Poppitz 2014
SU(2) and are exception: second order transition
Lattice simulations for SU(2), SU(N>2) and Sp(4) indicated second order for SU(2), first order for
SU(N>2) and Sp(4) (Holland, Pepe, and Wiese 2003)
SU(2)SU(2)Spin(4)
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Phase transitions in pure YM
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String tension
rLe (0)(x)trtr
Compare latticeSimulations: Bicudo 2010done for SU(3)
Discontinuous transition
Same behavior for SU(3)
S
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Phase transitions in pure YM
Topological angle:
Compare lattice studies for SU(3): Bonati, D’Elia, Panagopoulos, Vicari 2013
SU(3)
cTT]tr[
M. A. 2013
mn
mnFF~
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Phase transitions in pure YM
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Take home messages
Mass deformed SUSY is a great tool to study pure YM
No single test has failed!
Continuity? (see the resurgence talks)
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Part III: Deconfinementtransition in QCD(adj) on
13 SR
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Thermal QCD(adj) on
At finite temperature we compactify the time direction
L1/T
1LT
2R
2T/1
identified
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2 rg
log1
2
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M.A., E. Poppitz, M. Unsal, 2011
13 SR
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Thermal QCD(adj) on
The story has one more twist!
At finite temperature, the W’s and charged fermions are important
TmWe/
density
r
W W
rg log2
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Electric charge
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13 SR
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Thermal QCD(adj) on
2-D Coulomb gas
22
2
2
2
2
2
2
2
22
2
2
2
2
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rlog
rlog
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13 SR
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Thermal QCD(adj) on
The partition function for SU(2)
BAbjaij
A
i
aAa
j
B
i
ABA
j
b
i
aba
ia Ai
Ai
ai
NNqqWW
NN
bionbion
NN
RRqiq
RRLT
qqgRR
g
qLTq
RdRdNNNNZ
WNWNbionbionAa
Wi
Wi
W
bioni
bioni
bion
,,,,
susy
2
2
,
22
,,
partscalar 4
log2
log32
exp
!!!!,,,
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Non-SUSY e-m duality Weakly coupled self-dual point
13 SR
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Mapping QCD(adj) to spin models
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This 2D Coulomb gas is EXACTLY equivalent to XY-spin models:
susy
partscalar )4cos()cos(
i
i
SS
ij
ji BAH
ji
Nearest neighbor interaction
External field
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Results for thermal QCD(adj) on
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Analytic results for non-SUSY SU(2) indicate a second transition deconfinement
Numerical results for SUSY SU(2) indicate a second order transition
13 SR
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Results for thermal QCD(adj) on
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XY-model simulations SUSY SU(2)
13 SR
M. Anber, S. Collier, S. Strimas-Mackey, E. Poppitz, B, Teeple, 2013
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Results for thermal QCD(adj) on
Results for nonsusy SU(3): phase coexistence at the critical temperature:
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13 SR
M. Anber, S. Collier, E. Poppitz, 2013
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Summary of the deconfinement picture
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Results for thermal QCD(adj) on
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The transition in QCD(adj) on
Second order for SU(2)
First order for SU(3)
Compare with lattice results of QCD(adj) on
Second order for SU(2) SUSY, G. Bergner, P. Giudice, G. Munster,
S. Peimont, S. Sandbrink 2014
First order for SU(3), Karsch and Lutgemeir 1998
13 SR
4R
13 SR
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Results for thermal QCD(adj) on
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Take home messages
The order of the transition is the same for and
Is there a deep reason? Continuity?
13 SR
13 SR
4R
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Conclusion
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New insights from studying this class of theories
Continuity? More tests are needed
More lattice studies are needed, can we see the composite strings?
Plenty of other works regarding compact theories on a circle (need for more future workshops)
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Appendix
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To study phase transitions order parameter
E.g. to study magntization in 2D
is invariant under
order parameter
,,
cos.x
xx
x
xx SSH
cSO :2H
x
i xeM
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Appendix
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Demagnetized phase and is unbroken
Magnetized phase and is broken
0M 2SO
0M 2SO
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Appendix
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Order parameter for pure YM: Polyakov loop
is gauge invariant:
s
dxAi
FFF pe00
trtrP
Thermal circle: compact time ncecircumfere
11
T
FP
0,, , , 0, 00
0
00
0
xUxUxUexUeAdxiAdxi
Gauge transformationsare periodic
UUUUAA
txAtxA ,,
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Appendix
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We can also consider Center transformations:
The center of a group are the elements that commute with all the elements in the group:
0,, xzUxU
Element of the center
gzzgGzZ ,
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Appendix
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For SU(N)
The Lagrangian invariant under the center
In the fundamental rep
1,...,1,0,
1
.
.
1
1
2
Nkez
NN
N
ki
k
FF zPP
aa FF