Searching for the Conformal Window Work in collaboration with A. Deuzeman and M. P. Lombardo Elisabetta Pallante e.pallante@rug.nl Rijksuniversiteit Groningen

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

Everything started when ….

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

? ? 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

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

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?

Why this is interesting

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

Theory Analytical predictions

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 ?

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

Lattice Strategies

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

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.

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

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

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

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.

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

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]

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