1. Andrej Ficnar Columbia University Hard Probes 2010, Eilat, Israel October 12, 2010 Nonconformal Holography of Heavy Quark Quenching Andrej Ficnar, Jorge Noronha, Miklos Gyulassy

2. Outline Motivation Holography AdS/CFT in a nutshell Conformal (non)invariance Bottom-up approach Fitting the lattice (black hole engineering) Thermodynamics Polyakov loop Heavy quark energy loss Nonconformal drag force formula Results Nonconformal Holography of Heavy Quark Quenching | Andrej Ficnar | HP 2010 2/13

3. Motivation QGP behaves as near-ideal fluid Luzum & Romatschke, 2008  Naturally implies strong coupling 3/13 Nonconformal Holography of Heavy Quark Quenching | Andrej Ficnar | HP 2010

4. AdS/CFT in a nutshell Formal equivalence of (3+1)-dim SYM and type IIB string theory defined on Holographic dictionary: In this way, one can study strongly coupled gauge theories ( ) by studying classical two-derivative (super)gravity Goal: understand finite temperature QCD using thermal SYM Problem: conformal invariance of SYM trivial vanishing trace anomaly... controls quantum string effects, want controls higher curvature contributions, want solution: take t’Hooft limit: Maldacena, 1998 4/13 Nonconformal Holography of Heavy Quark Quenching | Andrej Ficnar | HP 2010

5. Conformal (non)invariance Lattice results show significant violation of conformal invariance near So start by solving the problem of conformal noninvariance: Holographic dictionary: Therefore, let’s look for models with nontrivial dilaton profile Borsányi et al., 2010 scalar field (dilaton) in the bulk dual operator in the gauge theory (“at the boundary”) Gubser et al., 2008Kiritsis et al., 2008 5/13 Nonconformal Holography of Heavy Quark Quenching | Andrej Ficnar | HP 2010

6. Bottom-up approach Task: construct an effective potential for the dilaton, which reproduces the expected phenomenology of the dual theory: induces a relevant deformation of the CFT: Form of the potential constrained by phenomenology and numerical factors are fitted to the lattice data: We require that the potential gives asymptotically ( ) - dual theory is conformal in the UV, but not asymptotically free ( finite)  applicability of the model restricted to close to interpolates between asymptotically AdS and a non conformal - gives determines fine tune of crossover 6/13 Nonconformal Holography of Heavy Quark Quenching | Andrej Ficnar | HP 2010

7. Fitting the lattice Solve EOMs using the following ansatz: Use the speed of sound to determine the ‘critical’ temperature: Bazavov et al., 2009 Borsányi et al., 2010 Works amazingly well! Gubser & Nellore, 2008 7/13 Nonconformal Holography of Heavy Quark Quenching | Andrej Ficnar | HP 2010 Wuppertal-Budapest hotQCD

8. Fitting the lattice By fitting just, all the other thermodynamic quantities are automatically fitted, e.g. trace anomaly We will directly see how the trace anomaly modifies the heavy quark energy loss 8/13 Nonconformal Holography of Heavy Quark Quenching | Andrej Ficnar | HP 2010 Wuppertal-Budapest hotQCD

9. Heavy quark energy loss Quark of mass is dual to the curved string in the bulk stretching from a D4 brane at to the horizon Generalized result for the energy loss (‘drag force’): Here is the coupling between the string and the dilaton, originating from the classical Nambu-Goto action for the string: Prediction from non-critical string theory: induced metric on the worldsheet Kiritsis et al., 2008 direct dependence on the medium properties 9/13 Nonconformal Holography of Heavy Quark Quenching | Andrej Ficnar | HP 2010

10. Polyakov loop fixes the α’ Polyakov loop is related to the free energy of a single heavy quark: Therefore, we can actually constrain in our model by fitting the Polyakov loop to the lattice data α’- corrections are important and should be explicitly calculated 10/13 Nonconformal Holography of Heavy Quark Quenching | Andrej Ficnar | HP 2010 Wuppertal-Budapest hotQCD Maldacena, 1998

11. Heavy quark energy loss: results 11/13 Nonconformal Holography of Heavy Quark Quenching | Andrej Ficnar | HP 2010 Wuppertal-Budapest hotQCD

12. Heavy quark energy loss: results 11/13 Nonconformal Holography of Heavy Quark Quenching | Andrej Ficnar | HP 2010 Wuppertal-Budapest hotQCD Effect of ?

13. Heavy quark energy loss: results 11/13 Nonconformal Holography of Heavy Quark Quenching | Andrej Ficnar | HP 2010 Wuppertal-Budapest hotQCD Effect of ? c/b ratio sensitive to the trace anomaly

14. Heavy quark energy loss: results 12/13 Nonconformal Holography of Heavy Quark Quenching | Andrej Ficnar | HP 2010 Wuppertal-Budapest hotQCD

15. Conclusions and Outlook Gauge/string duality gives us means to address the violation of conformal invariance near and see how the trace anomaly affects the energy loss Details of EOS are important for heavy quark energy loss in the crossover region (close to ) In this model, the energy loss of heavy quarks is a prediction Things to do: with initial conditions and full expanding geometry - corrections for thermodynamics and the energy loss Extra field for modeling the chiral phase transition in QCD Nonzero Gluon energy loss 13/13 Nonconformal Holography of Heavy Quark Quenching | Andrej Ficnar | HP 2010