h unting for the c onformal w indow in a foggy day …
DESCRIPTION
H unting for the C onformal W indow in a foggy day …. Work in collaboration with A. Deuzeman and M. P. Lombardo. Elisabetta Pallante. [email protected]. Rijksuniversiteit Groningen. O utline. Why this is interesting The conformal phase and its sorroundings - PowerPoint PPT PresentationTRANSCRIPT
HHuntingunting for thefor the
CConformalonformal WWindowindow in a foggy dayin a foggy day
… … Elisabetta PallanteElisabetta PallanteRijksuniversiteit [email protected]
Work in collaboration with A. Deuzeman and M. P. Lombardo
Why this is interestingWhy this is interesting
The conformal phase and its The conformal phase and its sorroundingssorroundings
Our story: it all started looking at a Our story: it all started looking at a plotplot
What theory can sayWhat theory can say
Lattice strategies: Lattice strategies: looking through looking through the fogthe fog
State of the art and outlookState of the art and outlook
OOutlineutline
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
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
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
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
Where do we stand ?Where do we stand ?
lattice
Nf
Is Nf=12 the lower end point of the conformal window ??
Nf = 8 is QCD-like
How to connect QCD-like theories with different flavour content?
0 4 8 12 160
2
4
6
8
Deuzeman, Lombardo, EP arXiv:0804.2905
A beautiful evidence of a first order transitionA beautiful evidence of a first order transition for eight flavoursfor eight flavours
The theory with eight flavours is still in the normal phase of QCD and shows a first order deconfining and chiral transition at T>0
[Deuzeman, Lombardo, EP arXiv:0804.2905]
The HysteresisThe Hysteresis
The cumulant R and The cumulant R and chiral susceptibilitieschiral susceptibilities
Asymptotic scalingAsymptotic scaling
Conclusive evidence of a thermal transition from two temporal extents Nt = 6 and 12
Towards the conformal phaseTowards the conformal phase
1. The study of bulk thermodynamic observables is a powerful strategy.
2. The improvement of the lattice fermion action with reducing
violations of asymptotic scaling is crucial for the success of the study of the chiral phase boundary.
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]
Conformality and sorroundingsConformality and sorroundings
Miransky, Yamawaki, arxiv: hep-th/9611142
Bulk PT – 1st order
Nf>Nfc
No AFDiffer in short distancebehaviour
Strong couplingNf*=8.05
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 (with CAVEATS)
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=12 (am=0.05)=12 (am=0.05)
• 123 x 16
Spatial volume dependence Mass dependence Complete scaling study
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 = 3.0, am=0.01, 0.015, 0.02, 0.025
Understand the nature of the two transitions with a combined set of observations.
Repeat the exercise at Nf=16. Old work by Damgaard et al.
Caveat on improvement for theories not asymptotically free.
Currently looking at the mass dependence of the chiral Condensate between the two transitions.
Perturbative
We are maybe collecting the right lights to look We are maybe collecting the right lights to look through the fog of the conformal window……through the fog of the conformal window……
Immediate aim: establish the nature of the two Immediate aim: establish the nature of the two transitionstransitions
Is NIs Nff=12 the lower end point ? =12 the lower end point ?
Shape of the chiral phase boundary (improvement!)Shape of the chiral phase boundary (improvement!)
Fractional flavours (staggered under scrutiny)Fractional flavours (staggered under scrutiny)
OOutlookutlook
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
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