Presentation on theme: "The fast life of holographic mesons (Rowan Thomson, Andrei Starinets & David Mateos) TexPoint fonts used in EMF. Read the TexPoint manual before you delete."— Presentation transcript:
The fast life of holographic mesons (Rowan Thomson, Andrei Starinets & David Mateos) TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA A A A AAA A A A with Aninda Sinha [arXiv:0803.nnnn]
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)
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 some strongly-coupled guage theories, e.g., Type IIb strings on AdS 5 X S 5 with RR flux N C D=4 N =4 U(N C ) super-Yang-Mills limited to: large N C and large ’t Hooft coupling sugra
QCD N =4 SYM confinement, discrete spectrum, scattering,.... conformal, continuous spectrum, no S-matrix, SUSY,.... very different !! T=0 strongly-coupled plasma of gluons & adjoint matter strongly-coupled plasma of gluons & fundamental matter deconfined, screening, finite corr. lengths,... deconfined, screening, finite corr. lengths,... T>T C T>>T C very similar !! runs to weak coupling remains strongly-coupled very different !!
Reality check? Is this more than hot air? Karsch (hep-lat/0106019)
0.75 1 143 2 T/T c ε/ε0ε/ε0 N=4 SYM (Gubser, Klebanov & Peet hep-th/9602135) scale energy density by free result Reality check? Is this more than hot air? Karsch (hep-lat/0106019)
0.75 1 143 2 RHIC ε/ε0ε/ε0 N=4 SYM scale energy density by free result “80% is closer to 75% than 100%” Strongly coupled QGP seems to be “conformal”, just above T c LHC T/T c
AdS/CFT : RHIC data : small Consider shear viscosity: (Kovtun, Son & Starinets hep-th/0309213; hep-th/0405231) (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 to sQGP Present exploration towards adding “fundamental” matter
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”:
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 relations: quasi-particle widths increase dramatically near
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 )
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 )
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
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
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]
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?
Spectral functions: diagnostic for “meson dissociation” simple poles in retarded correlator: yield peaks: “quasi-particle” if characteristic high “frequency” tail:
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”
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→∞):
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
See also: Erdmenger, Kaminski & Rust [arXiv:0710.033] Increasing n q, increases width of meson states Spectral functions: n q = 0 = 0.06 = 0.15 = 0.25 at rest: q=0
Spectral functions: follow positions of peaks real part of quasiparticle frequency, Ω(q) (n q = 0.25)
Spectral functions: follow positions of peaks real part of quasiparticle frequency, Ω(q) (n q = 0.25) v lim = 0.995 (calculated for n q =0) Quasiparticles obey same speed limit!
follow widths of peaks imaginary part of quasiparticle frequency, Γ(q) v lim =.995 =.651 =.343 =.651
examine Schrodinger potential for quasinormal modes
Quasiparticles limited to maximum momentum q max (define q max as value where V eff has inflection point) continuous curves fit with form: n q = 0.0001 = 0.0005 = 0.25
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? D3/D7 system: interesting framework to study quark/meson contributions to strongly-coupled nonAbelian plasma “speed limit” universal for holographic theories quasiparticle widths increase dramatically with momentum more analytic control; quasinormal spectrum find in present holographic model universal behaviour? real world effect? ( INVESTIGATING) extended excitations? QCD??
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