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H unting for the C onformal W indow in a foggy day …

H unting for the C onformal W indow in a foggy day …. Work in collaboration with A. Deuzeman and M. P. Lombardo. Elisabetta Pallante. e.pallante@rug.nl. Rijksuniversiteit Groningen. O utline. Why this is interesting The conformal phase and its sorroundings

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H unting for the C onformal W indow in a foggy day …

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  1. Huntingfor theConformal Window in a foggy day… Work in collaboration with A. Deuzeman and M. P. Lombardo Elisabetta Pallante e.pallante@rug.nl Rijksuniversiteit Groningen

  2. Outline 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

  3. Why this is interesting

  4. 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

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

  6. Everything started when ….

  7. The Plot 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

  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 ? b lattice Is Nf=12 the lower end point of the conformal window ?? Nf Nf = 8 is QCD-like Deuzeman, Lombardo, EP arXiv:0804.2905 How to connect QCD-like theories with different flavour content?

  10. Eight Flavours

  11. A beautiful evidence of a first order transition 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 cumulant R and chiral susceptibilities The Hysteresis

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

  14. The Scaling plot

  15. Towards the conformal phase • 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 Analytical predictions

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

  18. 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: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 b function • Ladder approximation • Anomaly matching

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

  20. Lattice Strategies

  21. 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:0806.1235[hep-ph] Thermodynamics Quark potential AFN, PRL, arXiv:0712.0609[hep-ph] Our program

  22. andNCF Need: broad range of volumes light quark masses many flavours algorithms highly improved actions (with CAVEATS) 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) Thank to the MILC Collaboration author of the MILC code.

  23. Phase transition at Nf=12 (am=0.05) • 123 x 16 • Spatial volume dependence • Mass dependence •  Complete scaling study

  24. Chiral condensate: Nt=8, 16

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

  26. Simulations at b = 2.750

  27. Understand the nature of the two transitions with a combined set of observations. Currently looking at the mass dependence of the chiral Condensate between the two transitions. Repeat the exercise at Nf=16. Old work by Damgaard et al. Perturbative Caveaton improvement for theories not asymptotically free.

  28. Outlook 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 Nf=12 the lower end point ? Shape of the chiral phase boundary (improvement!) Fractional flavours (staggered under scrutiny)

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

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

  31. The Scaling plot

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

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

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