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The fast life ofholographic mesons
(Rowan Thomson, Andrei Starinets & David Mateos)
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-coupledsystems 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-coupledsystems are very limited (e.g., nonexistent)
AdS/CFT correspondence provides simple tools to studysome strongly-coupled guage theories, e.g.,
Type IIb stringson 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
sugra
QCD N=4 SYM
confinement,discrete spectrum,
scattering, . . . .
conformal,continuous spectrum,
no S-matrix, SUSY, . . . .
very different !!
T=0
strongly-coupled plasmaof gluons & adjoint matter
strongly-coupled plasmaof gluons & fundamental matter
deconfined, screening,finite corr. lengths, . . .
deconfined, screening,finite corr. lengths, . . .
T>TC
T>>TC
very similar !!
runs to weak coupling remains strongly-coupled
very different !!
0.75
1
1 432 T/Tc
ε/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
1 432
RHIC
ε/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 Tc
LHC
T/Tc
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(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 relations:
quasi-particle widths increase dramatically near
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]
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]
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”
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 = 0.06 = 0.15 = 0.25
at rest: q=0
Spectral functions:
follow positions of peaksreal part of quasiparticle frequency, Ω(q)
(nq = 0.25)
vlim = 0.995
(calculated for nq=0)
Quasiparticles obey same speed limit!
follow widths of peaksimaginary part of quasiparticle frequency, Γ(q)
vlim = .995 = .651 = .343 = .651
Quasiparticles limited to maximum momentum qmax
(define qmax as value where Veff has inflection point)
continuous curves fit with form:
nq = 0.0001 = 0.0005 = 0.25
Conclusions/Outlook:
• first order phase transition appears as universal feature of holographic theories with fundamental matter (Tf > Tc) 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??