HHuntingunting for thefor the

CConformalonformal WWindowindow in a foggy dayin a foggy day

… … Elisabetta PallanteElisabetta PallanteRijksuniversiteit Groningene.pallante@rug.nl

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

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

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

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

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

Eight FlavoursEight Flavours

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

The Scaling plotThe Scaling plot

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.

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]

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

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 (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

Chiral condensate: NChiral condensate: Ntt=8, 16=8, 16

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

Simulations at = 2.750

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

The Scaling plotThe Scaling plot

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]