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Spectral functions for holographic mesons

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

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Spectral functions for holographic mesons

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

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

  3. 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”:

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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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.)

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

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

  12. 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] In experiments (eg, RHIC or LHC), these bound states are created with finite (possibly large) momenta. Does “speed limit” apply to heavy quark states in QCD?

  13. 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]

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

  15. 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

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

  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 D7-brane gauge field: asymptotically (ρ→∞): electric field lines can’t end in empty space; nqproduces neck BH embedding with tunable horizon

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

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

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

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

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

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

  25. examine Schrodinger potential for quasinormal modes

  26. Quasiparticles limited to maximum momentum qmax

  27. 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? • should survive finite 1/Nc, 1/λ, Nf/Nc corrections • interesting question for lattice investigations • “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: • one of most striking features of transition is “meson melting”: black hole: continuous gapless excitations Minkowski: discrete stable states • in a confining theory, will have two phase transitions • for sufficiently heavy quarks • feature of QCD ?? • simple physical picture: Matsui & Satz structure functions reveal: (Hong, Yoon & Strassler) Wilson lines reveal: (Rey, Theisen & Yee) mesons dissociate:

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

  31. Reminder about large N counting: entropy density: 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. minimizing free energy (euclideanbrane action) fixes physical configuration physical properties of thermal system are multi-valued critical embedding Minkowski embeddings phase transition See also: Babington et al (hep-th/0306018) BH embeddings Kirsch (hep-th/0406274)

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

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

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