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T he bulk transition of many flavour QCD and the S earch for an UVFP at strong coupling

This work explores the bulk transition of many-flavor QCD and searches for a UVFP at strong coupling. It investigates the theoretical motivation, lattice results, and conformal window of this transition. The study also considers the lines of phase transitions and the AdS/CFT-inspired scenario with a Conformal Window.

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T he bulk transition of many flavour QCD and the S earch for an UVFP at strong coupling

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  1. The bulk transition of many flavour QCD and the Search for an UVFP at strong coupling Work in collaboration with A. Deuzeman and M. P. Lombardo

  2. Outline Theoretical motivation The bulk transition with 12 flavours First order, second order, crossover? Lattice results

  3. Conformal Window Nf UVFP IRFP Conformal PT QCD g( Lattice) An UVFP at strong coupling (?) Lines of Phase Transitions

  4. Banks Zaks Miransky Yamawaki IRFP UVFP IRFP UVFP And with no Conformal Window (?) Lines of Phase Transitions

  5. AdS/CFT inspired scenario with a Conformal Window Kaplan et al, 2009 D++ D-=d=4 Strong coupling x= Nf/Nc Veneziano limit Disappearance Conformal Window = Annihilation of IR and UV pairs

  6. Comments and Caveats • The QCD dual at the UVFP is a new theory in the continuum • The coupling parameter space at the UVFP is enlarged • The anomalous dimension of the fermion mass operator is exactly gm=1 at the end-point of the CW for exact AdS/CFT • gm=1, where (ψ ψ)2 becomes relevant, is assumed in the Schwinger-Dyson equation to induce cSB and the disappearance of the CW  Nf ~ 12 at the CW end-point ? Chiral dynamics AdS/CFT(QCD)

  7. Comments and Caveats • The UV and IR annihilation mechanism may just be realized at the CW end-point = critical point. • The chiral condensate is the order parameter of all the identified phase transition lines

  8. Lattice Strategy

  9. Identify Nf conformal Look for chiral T=0 phase transitions and identify their nature UVFP  second order chiral transition

  10. Historical Question (Lattice QED) Should we add by hand new (relevant) operators on the lattice to capture phase transitions of the strongly coupled theory and their nature ?

  11. Zoom in the bulk transition at Nf=12 Deuzeman, Lombardo EP, 2009

  12. Nt dependence: Thermal versus Bulk . . . 0 to 1

  13. Chiral Condensate: Mass dependence Two sharp jumps at lighter masses The transition moves: lower mass stronger coupling

  14. Plaquette: Mass dependence Plaquette jumps overlap with condensate jumps (further confirmation of bulk nature+hints to first order)

  15. Connected susceptibility: mass dependence

  16. Connected susceptibility: volume scaling Linear scaling with V hints at first order transition

  17. (Pseudo) Critical point: mass dependence (log-log) Weak coupling Strong coupling bc(m) (weak) = bc(0) + A*m  first order transition bc(m) (strong) seems not linear (preliminary)

  18. Connected susceptibility peaks: mass scaling splitting of the transition Confirms the linear behaviour of the weak coupling transition

  19. Thermalization/Metastabilities Polyakov loop at Nt=6 above and below bc am = 0.025 (caveat on Nt) Phase freezing at b=3.0 Nt=6, am =0.025 Signals of hysteresis: analysis in progress

  20. A summary of candidate scenarios 1. Weak coupling = UVFP Strong coupling = lattice induced  seems excluded 2. Inverse order of 1. seems not plausible 3. Weak coupling = first order/sharp chiral crossover Strong coupling = lattice artefact Possible causes: change of symmetry, anomalous breaking, taste breaking 4. Genuine confinement – chiral splitting, analogous to the QCD (thermal) phase transition

  21. QCD Phase Transition inspired scenarios bc (Tc) Confinement driven Tdecon m=∞ Chiral driven Tc m m=0 Crossover ``inversion’’ at m ≠ 0 possible action dependent

  22. Scenario 3 seems favoured by our preliminary data No emergence of an UVFP at strong coupling

  23. Outlook • Our (preliminary) data favour the following scenario at Nf=12 First order bulk Conformal PT Critical end-point

  24. Outlook • The annihilation mechanism can be realized at the end point of the CW  critical point • Improve study of disconnected susceptibility, plaquette variance, spectrum (Rpratio) • Establish the existence and properties of the Conformal PT • Compare with the PT structure and nature of Nf=16

  25. Condensate along bc

  26. Rp along bc

  27. Rp at fixed b

  28. Condensate at fixed b

  29. 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]

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