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

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

Why 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 reasons

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

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 Plot

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

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:

Eight Flavours

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: ]

The Hysteresis The cumulant R and chiral susceptibilities

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

The Scaling plot

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.

Theory Theory Analytical predictions

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 ?

Bounds on the conformal window 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  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]

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

Lattice Strategies

The physics at hand inspires lattice strategies Running coupling on the lattice The SF approach AFN, PRL, arXiv: [hep-ph] EOS counting d.o.f. Anomalous dimensions/ critical exponents Luty arXiv: [hep-ph] Thermodynamics Quark 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 N f =12 (am=0.05) 12 3 x 16  Spatial volume dependence  Mass dependence  Complete scaling study

Chiral condensate: N t =8, 16

The chiral condensate with the quark mass 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 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

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

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

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

The Scaling plot

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

Appelquist et al. arXiv: [hep-ph ]