The fast life of
holographic mesons
with Aninda Sinha [arXiv:0803.nnnn]
(Rowan Thomson, Andrei Starinets & David Mateos)
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.,
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
T=0
QCD
N=4 SYM
confinement,
discrete spectrum,
scattering, . . . .
conformal,
continuous spectrum,
no S-matrix, SUSY, . . . .
very different !!
T>TC
strongly-coupled plasma
strongly-coupled plasma
of gluons & fundamental matter of gluons & adjoint matter
deconfined, screening,
deconfined, screening,
finite corr. lengths, . . .
finite corr. lengths, . . .
very similar !!
T>>TC
runs to weak coupling
remains strongly-coupled
very different !!
Reality check? Is this more than hot air?
Karsch (hep-lat/0106019)
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 & Peet hep-th/9602135)
1
2
3
T/Tc
4
“80% is closer to 75% than 100%”
Strongly coupled QGP seems to be “conformal”, just above Tc
RHIC
LHC
1
scale energy density by free result
0.75
ε/ε0
N=4 SYM
1
2
3
T/Tc
4
Consider shear viscosity:
AdS/CFT :
(Kovtun, Son & Starinets hep-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 to sQGP
Present exploration towards adding “fundamental” matter
Field theory story: (Reader’s Digest version)
N =2 SU(Nc) super-Yang-Mills with (Nf+1) hypermultiplets
fundamental
adjoint fields: vector:
1 hyper:
fundamental fields: Nf massive hyper’s
2 complex scalars :
2 Weyl fermions:
adjoint
N =4 SYM
content
“quarks”
fund. in U(Nc)
& global U(Nf)
• work in limit of large Nc and large λ but Nf fixed
“quenched approximation”:
• note not a confining theory:
free quarks
“mesons” (f f bound states)
Finite Temperature:
• low temperatures:
free quarks
mesons ( f f bound states)
unusual dispersion relations:
quasi-particle widths increase dramatically near
• phase transition:
(strong coupling!!)
• high temperatures:
NO quark or meson quasi-particles
“quarks dissolved in strongly coupled plasma”
Aharony, Fayyazuddin & Maldacena (hep-th/9806159 )
Karch & Katz (hep-th/0205236 )
Adding flavour to AdS/CFT
add Nf probe D7-branes
equator
AdS5 boundary
S5
D7
S3
horizon
Free quarks appear with mass:
pole
Aharony, Fayyazuddin & Maldacena (hep-th/9806159 )
Karch & Katz (hep-th/0205236 )
Adding flavour to 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
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 linearized eq’s of motion by separation of variables
Veff
Discrete spectrum:
r
= radial AdS #
= angular # on S3
Gauge/Gravity thermodynamics:
Witten (hep-th/9803131); …..
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
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
D3
Minkowski embedding
raise T: horizon expands and increased gravity
pulls brane towards BH horizon
Low T: tension supports brane;
D7 remains outside BH horizon
Black hole embedding
Phase transition†
High T: gravity overcomes tension;
D7 falls through BH horizon
(†This new phase transition is not a deconfinement transition.)
Mesons in Motion:
Mateos, RCM &Thomson [hep-th/0701132]
Ejaz, Faulkner, Liu, Rajagopal & Wiedemann [arXiv:0712.0590]
pseudoscalar
scalar
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]
’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]
Spectral functions:
diagnostic for “meson dissociation”
• simple poles in retarded correlator:
yield peaks:
“quasi-particle” if
• characteristic high “frequency” tail:
Spectral functions:
diagnostic for “meson dissociation”
hi-freq tail
discrete spectrum;
low temperature Mink. phase
mesons stable (at large Nc)
continuous spectrum;
high temperature BH phase
no quasi-particles
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
D7-brane gauge field:
asymptotically (ρ→∞):
electric field lines can’t end in empty
space; nq produces neck
BH embedding with tunable horizon
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]
Spectral functions:
introduce nonvanishing momentum
(nq = 0.25)
Spectral functions:
(nq = 0.25)
follow positions of peaks
real part of quasiparticle frequency, Ω(q)
(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!
follow widths of peaks
imaginary part of quasiparticle frequency, Γ(q)
vlim = .995
= .651
= .343
= .651
examine Schrodinger potential for quasinormal modes
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:
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)