Searching

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Searching for the Conformal Window
Work in collaboration with A. Deuzeman and M. P.
Lombardo
Elisabetta Pallante
Rijksuniversiteit Groningen
e.pallante_at_rug.nl
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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
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Everything started when .
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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
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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 Nf16.5
Conformal window T 0
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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
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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?
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Why this is interesting
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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
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Theory Analytical predictions
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The 2 loop running of the coupling constant
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Bounds on the conformal window
Nfc 12
Nfc 8.25
N3
Plot from Ryttov, Sannino, 2007
An upper bound is predicted of Nfc lt 11.9
Ryttov, Sannino arXiv0711.3745 hep-th Ryttov,
Sannino arXiv0707.3166 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
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Lattice Strategies
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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
arXiv0806.1235hep-ph
Thermodynamics Quark potential
AFN, PRL, arXiv0712.0609hep-ph
Our program
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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)
Thank to the MILC Collaboration author of the
MILC code.
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Phase transition at Nf4 (am0.01)
V203X6
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Phase transition at Nf4 (am0.02)
V123X6
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Phase transition at Nf12 (am0.05)
BULK
83 x 12 123 x 16
? Spatial volume dependence ? Complete scaling
study
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Outlook
The study of Nf12 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.
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The chiral condensate with the quark mass
Simulations at b 3.0, am0.01, 0.015, 0.02,
0.025
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Supersymmetric
Non supersymmetric
Appelquist, Cohen, Schmaltz, 1999
Duality arguments determine the extent of the
conformal window
Seiberg 1995
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Appelquist et al. arXiv0712.0609 hep-ph