1. Searching for the Conformal Window
Work in collaboration with A. Deuzeman and M. P. Lombardo
Elisabetta Pallante
Rijksuniversiteit Groningen

2. Outline The story: it all started looking at a plot
Our program (and main results)
Why this is interesting
What theory can say
Lattice strategies
Results and outlook

3. Everything started when ….

4. The Plot It predicts the shape of the chiral phase boundary
Braun, Gies JHEP06 (2006) 024
It predicts the shape of the chiral phase boundary
~ linear
It relates two universal quantities: the phase boundary and
the IR critical exponent of the running coupling

5. ? ? Simple questions with difficult answers
Is the conformal symmetry restored before the loss
of asymptotic freedom?
Banks, Zaks NPB 196 (1982) 189 ?
Plasma phase
Conformal Phase
chiral boundary ?
Lower-end
Loss of asymptotic
freedom at Nf=16.5
Conformal window T = 0

6. Our 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

7. Anticipating the end of the talk …
b lattice
Bulk transition ?! Nf
Talk by A. Deuzeman at the end of this session
How to connect QCD-like theories with different flavour content?

8. Why this is interesting

9. Three reasons Strongly interacting physics beyond the Standard Model.
Walking Technicolor? Composite Higgs?
Understanding the quark-gluon
plasma phase.
ALICE at CERN LHC
Bridging field theory to string theory via the AdS/CFT
correspondence

10. Theory
Analytical predictions

11. The 2 loop running of the coupling constant
Conjecture
at strong-coupling
Non-trivial IR fixed-point
appears at Nf = 8.05
g(Q) ~ g* ~ const
IRFP ?

12. Bounds on the conformal window
Nfc ~ 12
Nfc = 8.25
N=3
[Plot from Ryttov, Sannino, 2007]
An upper bound is predicted of Nfc <= 11.9
Ryttov, Sannino arXiv: [hep-th]
Ryttov, Sannino arXiv: [hep-th]
Appelquist et al., PRD 60 (1999)
Appelquist et al., PRD 58 (1998)
• SUSY inspired all order b function
• Ladder approximation
• Anomaly matching

13. Lattice Strategies

14. The physics at hand inspires lattice strategies
EOS
counting d.o.f.
Running coupling
on the lattice
The SF approach
Anomalous dimensions/
critical exponents
Luty arXiv: [hep-ph]
Thermodynamics
Quark potential
AFN, PRL, arXiv: [hep-ph]
Our program

15. Need: broad range of volumes
light quark masses
many flavours algorithms
highly improved actions
Use: MILC code with small additions
Staggered AsqTad +one loop Symanzik improved action
RHMC algorithm
Machines: Huygens at SARA (P5+ upgraded to P6)
BlueGene L at ASTRON/RUG (upgraded to BG/P)
and NCF
Thank to the MILC Collaboration author of the MILC code.

16. Phase transition at Nf=4 (am=0.01)
V=203X6

17. Phase transition at Nf=4 (am=0.02)
V=123X6

18. Phase transition at Nf=12 (am=0.05) BULK …
• 83 x 12
• 123 x 16
 Spatial volume dependence
 Complete scaling study

19. Outlook The study of Nf=12 is being completed.
Locate the lower end of the conformal window.
Further explore its properties.
Shape the chiral phase boundary.
Fractional flavours (staggered under scrutiny)
Highly improved actions are essential for this to work.

20. The chiral condensate with the quark mass
Simulations at b = 3.0, am=0.01, 0.015, 0.02, 0.025

21. Supersymmetric Non supersymmetric Upper limit on the threshold of CW
[Appelquist, Cohen, Schmaltz, 1999]
Duality arguments determine the extent of the conformal window
[Seiberg 1995]

22. Appelquist et al. arXiv:0712.0609 [hep-ph]