s earching for the c onformal w indow
DESCRIPTION
S earching for the C onformal W indow. Work in collaboration with A. Deuzeman and M. P. Lombardo. Elisabetta Pallante. [email protected]. Rijksuniversiteit Groningen. O utline. The story: it all started looking at a plot Our program (and main results) Why this is interesting - PowerPoint PPT PresentationTRANSCRIPT
SSearching earching
for the for the CConformal onformal
WWindowindow
Elisabetta PallanteElisabetta Pallante
Rijksuniversiteit [email protected]
Work in collaboration with A. Deuzeman and M. P. Lombardo
The story: it all started looking at a The story: it all started looking at a plotplot
Our program (and main results)Our program (and main results)
Why this is interestingWhy this is interesting
What theory can sayWhat theory can say
Lattice strategiesLattice strategies
Results and outlookResults and outlook
OOutlineutline
Everything started when ….
Braun, Gies JHEP06 (2006) 024
It relates two universal quantities: the phase boundary and the IR critical exponent of the running coupling
It predicts the shape of the chiral phase boundary
~ linear
The PlotThe Plot
Simple questions with difficult answersSimple questions with difficult answers
Is the conformal symmetry restored before the loss of asymptotic freedom?
Loss of asymptotic freedom at Nf=16.5
Banks, Zaks NPB 196 (1982) 189Banks, Zaks NPB 196 (1982) 189
Lower-end?
Conformal window T = 0
?Pla
sma
phase
Confo
rmal
Phas
e
chiral boundary
2 4 6 8 10 12 14 16
0
50
100
150
200
Quark Gluon Plasma
Hadronic Phase
T[M
eV]
N f
Our programOur program
1) The conformal window (lower end point)
2) The shape of the chiral phase boundary
3) The connection between the QGP phase and the conformal phase
4) Fractional flavours
Anticipating the end of the talk …Anticipating the end of the talk …
lattice
Nf
Bulk transition ?!
Talk by A. Deuzeman at the end of this session
How to connect QCD-like theories with different flavour content?
0 4 8 12 160
2
4
6
8
Why this is interestingWhy this is interesting
ALICE at CERN LHC
Strongly interacting physics beyond the Standard Model.Walking Technicolor? Composite Higgs?
Understanding the quark-gluon plasma phase.
Bridging field theory to string theory via the AdS/CFT correspondence
Three reasonsThree reasons
TheoryTheoryAnalytical predictionsAnalytical predictions
The 2 loop running of the coupling constantThe 2 loop running of the coupling constant
Conjectureat strong-coupling
Non-trivial IR fixed-point appears at Nf = 8.05
g(Q) ~ g* ~ const
IRFP
?
Bounds on the conformal windowBounds on the conformal window
Ryttov, Sannino arXiv:0711.3745 [hep-th]Ryttov, Sannino arXiv:0707.3166 [hep-th]Appelquist et al., PRD 60 (1999) 045003Appelquist et al., PRD 58 (1998) 105017
• SUSY inspired all order function• Ladder approximation• Anomaly matching
Nfc ~ 12
Nfc = 8.25
An upper bound is predicted of Nfc <= 11.9
N=3 [Plot from Ryttov, Sannino, 2007]
Lattice StrategiesLattice Strategies
The physics at hand inspires lattice strategiesThe physics at hand inspires lattice strategies
Running couplingon the lattice
The SF approach
AFN, PRL, arXiv:0712.0609[hep-ph]
EOScounting d.o.f.
Anomalous dimensions/critical exponentsLuty arXiv:0806.1235[hep-ph]
ThermodynamicsQuark potential
Our program
Need:Need: broad range of volumes light quark masses many flavours algorithms highly improved actions
Use:Use: MILC code with small additions Staggered AsqTad +one loop Symanzik improved action RHMC algorithm
Machines:Machines: Huygens at SARA (P5+ upgraded to P6) BlueGene L at ASTRON/RUG (upgraded to BG/P)
Thank to the MILC Collaboration author of the MILC code.
and NCF
Phase transition at NPhase transition at Nff=4 (am=0.01)=4 (am=0.01)
5.5 5.7 5.9 6.1 6.3 6.50.00
0.04
0.08
0.12
0.16
0.00
0.02
0.04
0.06
0.08
0.10
PB
P
Po
lyakov L
oo
p
V=203X6
Phase transition at NPhase transition at Nff=4 (am=0.02)=4 (am=0.02)
5.5 5.7 5.9 6.1 6.3 6.50.00
0.05
0.10
0.15
0.20
0.25
0.00
0.05
0.10
0.15
PB
PP
oly
ak
ov
Lo
op
V=123X6
Phase transition at NPhase transition at Nff=12 (am=0.05)=12 (am=0.05) BULK …BULK …
• 83 x 12• 123 x 16
Spatial volume dependence Complete scaling study
0 1 2 3 4 50.0
0.2
0.4
0.6
0.8
PB
P
Highly improved actions are essential for this to work.Highly improved actions are essential for this to work.
The study of Nf=12 is being completed.The study of Nf=12 is being completed.
Locate the lower end of the conformal window.Locate the lower end of the conformal window.
Further explore its properties.Further explore its properties.
Shape the chiral phase boundary.Shape the chiral phase boundary.
Fractional flavours (staggered under scrutiny)Fractional flavours (staggered under scrutiny)
OOutlookutlook
The chiral condensate with the quark massThe chiral condensate with the quark mass
0.00 0.01 0.02 0.030.00
0.02
0.04
0.06
0.08
am
Simulations at b = 3.0, am=0.01, 0.015, 0.02, 0.025
SupersymmetricSupersymmetric
Non supersymmetricNon supersymmetric
[Seiberg 1995]
Upper limit on the threshold of CW
[Appelquist, Cohen, Schmaltz, 1999]
Duality arguments determine the extent of the conformal window
Appelquist et al. arXiv:0712.0609 [hep-ph]