SSearching earching

for the for the CConformal onformal

WWindowindow

Elisabetta PallanteElisabetta Pallante

Rijksuniversiteit Groningene.pallante@rug.nl

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]