1. H unting for the C onformal W indow in a foggy day … in a foggy day … Elisabetta Pallante Rijksuniversiteit Groningene.pallante@rug.nl Work in collaboration with A. Deuzeman and M. P. Lombardo

2. Why this is interesting The conformal phase and its sorroundings Our story: it all started looking at a plot What theory can say Lattice strategies: looking through the fog State of the art and outlook O utline

3. Why this is interesting

4. 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 reasons

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

6. Everything started when ….

7. 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 Plot

8. 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

9. Where do we stand ?  lattice NfNf Is N f =12 the lower end point of the conformal window ?? N f = 8 is QCD-like How to connect QCD-like theories with different flavour content? Deuzeman, Lombardo, EP arXiv:0804.2905

10. Eight Flavours

11. A beautiful evidence of a first order transition for eight flavours for 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]

12. The Hysteresis The cumulant R and chiral susceptibilities

13. Asymptotic scaling Conclusive evidence of a thermal transition from two temporal extents N t = 6 and 12

14. The Scaling plot

15. Towards 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.

16. Theory Theory Analytical predictions

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

18. Bounds on the conformal window Ryttov, Sannino arXiv:0711.3745 [hep-th] Ryttov, Sannino arXiv:0707.3166 [hep-th] Appelquist et al., PRD 60 (1999) 045003 Appelquist et al., PRD 58 (1998) 105017 SUSY inspired all order  function Ladder approximation Anomaly matching N f c ~ 12 N f c = 8.25 An upper bound is predicted of N f c <= 11.9 N=3 [Plot from Ryttov, Sannino, 2007]

19. Conformality and sorroundings Miransky, Yamawaki, arxiv: hep-th/9611142 Bulk PT – 1 st order N f >N f c No AF Differ in short distance behaviour Strong coupling N f *=8.05

20. Lattice Strategies

21. The physics at hand inspires lattice strategies Running coupling on the lattice The SF approach AFN, PRL, arXiv:0712.0609[hep-ph] EOS counting d.o.f. Anomalous dimensions/ critical exponents Luty arXiv:0806.1235[hep-ph] Thermodynamics Quark potential Our program

22. 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

23. Phase transition at N f =12 (am=0.05) 12 3 x 16  Spatial volume dependence  Mass dependence  Complete scaling study

24. Chiral condensate: N t =8, 16

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

28. Simulations at  = 2.750

29. Understand the nature of the two transitions with a combined set of observations. Repeat the exercise at N f =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

30. We are maybe collecting the right lights to look through the fog of the conformal window…… Immediate aim: establish the nature of the two transitions Is N f =12 the lower end point ? Shape of the chiral phase boundary (improvement!) Fractional flavours (staggered under scrutiny) O utlook

31. Phase transition at N f =4 (am=0.01) V=20 3 X6

32. Phase transition at N f =4 (am=0.02) V=12 3 X6

33. The Scaling plot

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

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