The fast life of holographic mesons

1. The fast life of holographic mesons with AnindaSinha[arXiv:0803.nnnn] (Rowan Thomson, Andrei Starinets & David Mateos) TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAA

2. Behaviour (e.g., real-time dynamics) of strongly-coupled QCD plasma is of interest for RHIC and early universe cosmology Theoretical tools to study such strongly-coupled systems are very limited (e.g., nonexistent)

3. Behaviour (e.g., real-time dynamics) of strongly-coupled QCD plasma is of interest for RHIC and early universe cosmology Theoretical tools to study such strongly-coupled systems are very limited (e.g., nonexistent) AdS/CFT correspondence provides simple tools to study somestrongly-coupledguage theories, e.g., sugra Type IIb strings on AdS5 X S5 with RR flux NC D=4 N=4 U(NC) super-Yang-Mills limited to: large NC and large ’t Hooft coupling

4. QCD N=4 SYM confinement, discrete spectrum, scattering, . . . . conformal, continuous spectrum, no S-matrix, SUSY, . . . . T=0 very different !! strongly-coupled plasma of gluons & fundamental matter strongly-coupled plasma of gluons & adjoint matter T>TC deconfined, screening, finite corr. lengths, . . . deconfined, screening, finite corr. lengths, . . . very similar !! runs to weak coupling remains strongly-coupled T>>TC very different !!

5. Reality check? Is this more than hot air? Karsch (hep-lat/0106019)

6. Reality check? Is this more than hot air? Karsch (hep-lat/0106019) 1 scale energy density by free result 0.75 ε/ε0 N=4 SYM (Gubser, Klebanov & Peethep-th/9602135) 1 3 4 2 T/Tc

7. “80% is closer to 75% than 100%” Strongly coupled QGP seems to be “conformal”, just above Tc LHC RHIC 1 scale energy density by free result 0.75 ε/ε0 N=4 SYM 1 3 4 2 T/Tc

8. Consider shear viscosity: AdS/CFT : (Kovtun, Son & Starinetshep-th/0309213; hep-th/0405231) RHIC data : small (Romatschke & Romatschke arXiv:0706.1522; Song & Heinz arXiv:0709.0742; 0712.3715) AdS/CFT does not give identical physics to QCD, but may indicate universal behaviour, applicable tosQGP Present exploration towards adding “fundamental” matter

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

10. note not a confining theory: • free quarks • “mesons” ( bound states) Finite Temperature: • low temperatures: • free quarks • mesons ( bound states) Holographic Results unusual dispersion relations: quasi-particle widths increase dramatically near • phase transition: (strong coupling!!) • high temperatures: • NO quarkor meson quasi-particles • “quarks dissolved in strongly coupled plasma”

11. Aharony, Fayyazuddin & Maldacena (hep-th/9806159 ) Karch& Katz (hep-th/0205236 ) Adding flavourto AdS/CFT add Nf probe D7-branes equator AdS5 boundary S5 D7 S3 horizon Free quarks appear with mass: pole

12. Aharony, Fayyazuddin & Maldacena (hep-th/9806159 ) Karch& Katz (hep-th/0205236 ) Adding flavourto AdS/CFT add Nf probe D7-branes equator AdS5 boundary S5 D7 S3 horizon Mesons ( bound states)dual to open string states supported by D7-brane pole

13. Kruczenski, Mateos, RCM & Winters [hep-th/0304032] 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 linearizedeq’s of motion by separation of variables Veff r Discrete spectrum: = radial AdS # = angular # on S3

14. Witten (hep-th/9803131); ….. Gauge/Gravity thermodynamics: Gauge theory thermodynamics = Black hole thermodynamics • 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

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

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

17. holographic model shows bound states persist above Tc • and have interesting dispersion relation • lattice QCD indicates heavy quark bound states persist above Tc Asakawa & Hatsuda [hep-lat/0308034] Datta, Karsch, Petreczky & Wetzorke [hep-lat/0312037] ’s have finite width! but in Mink. phase, holographic mesons are absolutely stable (for large Nc) can we do better in AdS/CFT? Satz [hep-ph/0512217]

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

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

20. 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→∞):

21. 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→∞): electric field lines can’t end in empty space; nq produces neck BH embedding with tunable horizon

22. Spectral functions: Increasing nq, increases width of meson states nq = 0 = 0.06 = 0.15 = 0.25 at rest: q=0 See also: Erdmenger, Kaminski & Rust [arXiv:0710.033]

23. (nq = 0.25) Spectral functions: introduce nonvanishing momentum

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

25. (nq = 0.25) Spectral functions: follow positions of peaks real part of quasiparticle frequency, Ω(q) vlim = 0.995 (calculated for nq=0) Quasiparticles obey same speed limit!

26. follow widths of peaks imaginary part of quasiparticle frequency, Γ(q) vlim = .995 = .651 = .343 = .651

27. examine Schrodinger potential for quasinormal modes

28. Quasiparticles limited to maximum momentum qmax (define qmax as value where Veff has inflection point) nq = 0.0001 = 0.0005 = 0.25 continuous curves fit with form:

29. Conclusions/Outlook: • D3/D7 system: interesting framework to study quark/meson • contributions to strongly-coupled nonAbelian plasma • first order phase transition appears as universal feature of • holographic theories with fundamental matter (Tf> Tc) • how robust is this transition? • “speed limit” universal for holographic theories extended excitations? QCD?? • quasiparticle widths increase dramatically with momentum • more analytic control; quasinormal spectrum • find in present holographic model • universal behaviour? real world effect? (INVESTIGATING)