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Spectral functionsfor holographic mesons
with Rowan Thomson, Andrei Starinets[arXiv:0706.0162]
and other stuffVwith Aninda Sinha [arXiv:0801.nnnn]
Motivation:
Exploring AdS/CFT as a tool to studythe strongly coupled quark-gluon plasma
See Steve Gubser’s talk!
Field theory story:
N =2 SU(Nc) super-Yang-Mills with (Nf+1) hypermultiplets
Nf massive hyper’s “quarks”
2 complex scalars :2 Weyl fermions:
N =4 SYMcontent
fund. in U(Nc) & global U(Nf)
(Reader’s Digest version)
fundamental adjoint
adjoint fields: vector:
1 hyper:
fundamental fields:
• work in limit of large Nc and large λ but Nf fixed
“quenched approximation”:
• low temperatures: free quarks
mesons ( bound states)f f
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)f f
unusual dispersion relation:
Holographic Results
add Nf probe D7-branes
horizon
AdS5 boundary
pole
equator
S5
S3
D7
Free quarks appear with mass:
Karch & Katz (hep-th/0205236 )Adding flavour to AdS/CFT
Aharony, Fayyazuddin & Maldacena (hep-th/9806159 )
add Nf probe D7-branes
horizon
AdS5 boundary
pole
equator
S5
S3
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 themassless 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
Veff
rDiscrete spectrum:
Kruczenski, Mateos, RCM & Winters [hep-th/0304032]
= radial AdS #= angular # on S3
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 includecontributions of probe branes/fundamental matter
Gauge/Gravity thermodynamics with probe branes:
put D7-probe in throat geometry of black D3-braneSUSY 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]
Brane entropy:
1st order phase transition
Transition temperature:
Mateos, RCM &Thomson [hep-th/0605046 & hep-th/0701132]
Mesons in Motion:
pseudoscalar
scalar
Mateos, RCM &Thomson [hep-th/0701132]
Ejaz, Faulkner, Liu, Rajagopal & Wiedemann [arXiv:0712.0590]
Radial profile
k increasing
• 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]
Does “speed limit” apply to heavy quark states in QCD?
In experiments (eg, RHIC or LHC), these bound statesare created with finite (possibly large) momenta.
• 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]
Satz [hep-ph/0512217]
’s have finite width!
but in Mink. phase, holographic mesonsare absolutely stable (for large Nc)
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 Nc) no quasi-particles
hi-freq tail
Spectral functions: diagnostic for “meson dissociation”
• 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]
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; nq produces neck
D7-brane gauge field:
asymptotically (ρ→∞):
BH embedding with tunable horizon
See also: Erdmenger, Kaminski & Rust [arXiv:0710.033]
Increasing nq, increases width of meson states
Spectral functions:
nq = 0 = 0.001 = 0.05 = 0.25
at rest: q=0
See also: Erdmenger, Kaminski & Rust [arXiv:0710.033]
Increasing nq, increases width of meson states
Spectral functions:
nq = 0 = 0.001 = 0.05 = 0.25
at rest: q=0
Spectral functions:
follow positions of peaksreal part of quasiparticle frequency, Ω(q)
(nq = 0.25)
vmax = 0.9975
(calculated for nq=0)
Quasiparticles obey same speed limit!
Conclusions/Outlook:
• 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
• 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)
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”:
even with mq=0, hypermultiplets introduce non-vanishing -function; however, running of `t Hooft coupling vanisheswith large-Nc limit
More legal details:
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, . . . . )
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,
phase transition
physical properties of thermalsystem are multi-valued
minimizing free energy(euclidean brane action)
fixes physical configuration
criticalembedding
Minkowskiembeddings
BH embeddingsSee also:Babington et al (hep-th/0306018) Kirsch (hep-th/0406274)
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