1. Spectral functions for holographic mesons with Rowan Thomson, Andrei Starinets [arXiv:0706.0162] TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA A A A AAA A A A and other stuff V with Aninda Sinha [arXiv:0801.nnnn]

2. Motivation: Exploring AdS/CFT as a tool to study the strongly coupled quark-gluon plasma See Steve Gubser’s talk!

3. Field theory story: N =2 SU(N c ) super-Yang-Mills with (N f +1) hypermultiplets N f massive hyper’s “quarks” 2 complex scalars : 2 Weyl fermions: N =4 SYM content fund. in U(N c ) & global U(N f ) (Reader’s Digest version) fundamental adjoint adjoint fields: vector: 1 hyper: fundamental fields: work in limit of large N c and large λ but N f fixed “quenched approximation”:

4. low temperatures: free quarks mesons ( bound states) Finite Temperature: phase transition: high temperatures: NO quark or meson quasi-particles “quarks dissolved in strongly coupled plasma” (strong coupling!!) note not a confining theory: free quarks “mesons” ( bound states) unusual dispersion relation:

5. add N f probe D7-branes horizon AdS 5 boundary pole equator S5S5 S3S3 D7 Free quarks appear with mass: Karch & Katz (hep-th/0205236 ) Adding flavour to AdS/CFT Aharony, Fayyazuddin & Maldacena (hep-th/9806159 )

6. add N f probe D7-branes horizon AdS 5 boundary pole equator S5S5 S3S3 D7 Karch & Katz (hep-th/0205236 ) Adding flavour to AdS/CFT Mesons ( bound states) dual to open string states supported by D7-brane Aharony, Fayyazuddin & Maldacena (hep-th/9806159 )

7. Mesons: lowest lying open string states are excitations of the massless modes on D7-brane: vector, scalars (& spinors) (free) spectrum: expand worldvolume action to second order in fluctuations solve linearized eq’s of motion by separation of variables V eff r Discrete spectrum: Kruczenski, Mateos, RCM & Winters [hep-th/0304032] = radial AdS # = angular # on S 3

8. Gauge theory thermodynamics = Black hole thermodynamics Gauge/Gravity thermodynamics: Witten (hep-th/9803131); ….. Replace SUSY D3-throat with throat of black D3-brane Wick rotate and use euclidean path integral techniqes..... Extend these ideas to include contributions of probe branes/fundamental matter

9. Gauge/Gravity thermodynamics with probe branes: put D7-probe in throat geometry of black D3-brane SUSY embedding Minkowski embedding Black hole embedding T=0: “brane flat” Low T: tension supports brane; D7 remains outside BH horizon raise T: horizon expands and increased gravity pulls brane towards BH horizon High T: gravity overcomes tension; D7 falls through BH horizon D7 D3 Phase transition † ( † This new phase transition is not a deconfinement transition.) Mateos, RCM &Thomson [hep-th/0605046];..... Babington, Erdmenger, Evans, Guralnik & Kirsch [hep-th/0306018]

10. Brane entropy: 1 st order phase transition Transition temperature: Mateos, RCM &Thomson [hep-th/0605046 & hep-th/0701132]

11. Mesons in Motion: pseudoscalar scalar Mateos, RCM &Thomson [hep-th/0701132] Ejaz, Faulkner, Liu, Rajagopal & Wiedemann [arXiv:0712.0590] Radial profile k increasing

12. holographic model shows bound states persist above T c and have interesting dispersion relation lattice QCD indicates heavy quark bound states persist above T c Asakawa & Hatsuda [hep-lat/0308034] Datta, Karsch, Petreczky & Wetzorke [hep-lat/0312037] Does “speed limit” apply to heavy quark states in QCD? In experiments (eg, RHIC or LHC), these bound states are created with finite (possibly large) momenta.

13. holographic model shows bound states persist above T c and have interesting dispersion relation lattice QCD indicates heavy quark bound states persist above T c Asakawa & Hatsuda [hep-lat/0308034] Datta, Karsch, Petreczky & Wetzorke [hep-lat/0312037] Satz [hep-ph/0512217] ’s have finite width! but in Mink. phase, holographic mesons are absolutely stable (for large N c ) can we do better in AdS/CFT?

14. Spectral functions: diagnostic for “meson dissociation” simple poles in retarded correlator: yield peaks: “quasi-particle” if characteristic high “frequency” tail:

15. discrete spectrum; low temperature Mink. phase continuous spectrum; high temperature BH phase mesons stable (at large N c ) no quasi-particles hi-freq tail Spectral functions: diagnostic for “meson dissociation”

16. approaching phase transition, structure builds quasinormal frequencies approach real axis Thermal spectral function: subract off asymptotic tail: phase transition see also: Hoyos, Landsteiner & Montero [hep-th/0612169] RCM, Rowan Thomson & Andrei Starinets [arXiv:0706.0162]

17. Kobayashi, Mateos, Matsuura, RCM & Thomson [hep-th/0611099] Mateos, Matsuura, RCM & Thomson [arXiv:0709.1225];..... Need an extra dial: “Quark” density D7-brane gauge field: asymptotically (ρ→∞):

18. Kobayashi, Mateos, Matsuura, RCM & Thomson [hep-th/0611099] Mateos, Matsuura, RCM & Thomson [arXiv:0709.1225];..... Need an extra dial: “Quark” density electric field lines can’t end in empty space; n q produces neck D7-brane gauge field: asymptotically (ρ→∞): BH embedding with tunable horizon

19. See also: Erdmenger, Kaminski & Rust [arXiv:0710.033] Increasing n q, increases width of meson states Spectral functions: n q = 0 = 0.001 = 0.05 = 0.25 at rest: q=0

20. See also: Erdmenger, Kaminski & Rust [arXiv:0710.033] Increasing n q, increases width of meson states Spectral functions: n q = 0 = 0.001 = 0.05 = 0.25 at rest: q=0

21. Spectral functions: introduce nonvanishing momentum (n q = 0.25)

22. Spectral functions: follow positions of peaks real part of quasiparticle frequency, Ω(q) (n q = 0.25)

23. Spectral functions: follow positions of peaks real part of quasiparticle frequency, Ω(q) (n q = 0.25) v max = 0.9975 (calculated for n q =0) Quasiparticles obey same speed limit!

24. follow widths of peaks imaginary part of quasiparticle frequency, Γ(q) Γ(q) diverges at finite q max

25. examine Schrodinger potential for quasinormal modes

26. Quasiparticles limited to maximum momentum q max

27. Conclusions/Outlook: first order phase transition appears as universal feature of holographic theories with fundamental matter (T f > T c ) how robust is this transition? should survive finite 1/N c, 1/λ, N f /N c corrections interesting question for lattice investigations D3/D7 system: interesting framework to study quark/meson contributions to strongly-coupled nonAbelian plasma “speed limit” universal for quasiparticles in plasma quasiparticle widths increase dramatically with momentum find in present holographic model universal behaviour? real world effect? ( INVESTIGATING)

28. [extra slides]

29. Meson spectrum: Minkowski: discrete stable states black hole: continuous gapless excitations feature of QCD ?? in a confining theory, will have two phase transitions for sufficiently heavy quarks simple physical picture: Matsui & Satz (Hong, Yoon & Strassler) structure functions reveal: (Rey, Theisen & Yee) Wilson lines reveal: mesons dissociate: one of most striking features of transition is “meson melting”:

30. even with m q =0, hypermultiplets introduce non-vanishing -function; however, running of `t Hooft coupling vanishes with large-N c limit More legal details: with large but finite N c to avoid Landau pole need to introduce additional matter content at some large UV scale Probe approximation: N f /N c → 0 recall above construction does not take into account the “gravitational” back-reaction of the D7-branes! → at finite N f /N c back-reaction would cause singularity; introduce orientifold at large radius (see, however: Burrington et al; Kirsch & Vaman; Casero, Nunez & Paredes,.... )

31. entropy density: Reminder about large N counting: counts # of d.o.f. entropy density: counts # of d.o.f. in our limit, thermodynamics dominated by adjoint fields; we are calculating small corrections due to fundamental matter these dominate over quantum effects, eg, Hawking radiation,

32. phase transition physical properties of thermal system are multi-valued minimizing free energy (euclidean brane action) fixes physical configuration critical embedding Minkowski embeddings BH embeddings See also: Babington et al (hep-th/0306018) Kirsch (hep-th/0406274)

33. Brane entropy: 1 st order phase transition Transition temperature:

34. H Gauge theory entropy: λ enhanced over naïve large-N counting phase transition “small glitch in extensive quantities”