Spectral functions for holographic mesons

receptivetrucksMechanics

Oct 27, 2013 (3 years and 9 months ago)

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Spectral
functions

for holographic mesons

with Rowan Thomson, Andrei
Starinets

[
arXiv:0706.0162
]

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with
Aninda

Sinha

[
arXiv:0801.nnnn
]

Motivation:

Exploring
AdS
/CFT as a tool to study

the strongly coupled quark
-
gluon plasma

See Steve
Gubser’s

talk!

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 relation:

add
N
f

probe D7
-
branes

horizon

AdS
5

boundary

pole

equator

S
5

S
3

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

S
5

S
3

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]

Brane entropy:

1
st

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
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]

Does “speed limit” apply to heavy quark states in QCD?

In experiments (
eg
, RHIC or LHC), these bound states

are created with finite (possibly large)
momenta
.



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”



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;
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


= 0.001


= 0.05


= 0.25

at rest: q=0

See also:
Erdmenger
, Kaminski & Rust [arXiv:0710.033]

Increasing
n
q
, increases width of meson states

Spectral functions:

n
q

= 0


= 0.001


= 0.05


= 0.25

at rest: q=0

Spectral functions:

introduce
nonvanishing

momentum

(
n
q

= 0.25)

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
max

= 0.9975

(calculated for
n
q
=0)

Quasiparticles

obey same speed limit!

follow widths of peaks

imaginary part of
quasiparticle

frequency,
Γ
(q)

Γ(q) d
iverges

at finite
q
max

examine Schrodinger potential for
quasinormal

modes

Quasiparticles

limited to maximum momentum
q
max

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?


should survive finite 1/
N
c
, 1/
λ
,
N
f
/
N
c

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)

[extra slides]

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
m
q
=0,
hypermultiplets

introduce non
-
vanishing


-
function; however,
running of
`t
Hooft

coupling
vanishes

with large
-
N
c

limit

More legal
details:

w
ith large but finite
N
c

to avoid Landau pole need to

introduce additional matter content at some large UV scale

Probe approximation
:
N
f

/
N
c

→ 0

recall above
construction does not take into account the

“gravitational” back
-
reaction of the D7
-
branes!


at finite
N
f

/
N
c

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,

p
hase
transition

physical properties of thermal

system are multi
-
valued

minimizing free
energy

(
euclidean

brane

action)

fixes physical configuration

c
ritical

embedding

Minkowski

embeddings

BH embeddings

See also:

Babington et al (
hep
-
th
/0306018
)

Kirsch
(
hep
-
th
/0406274)

Brane entropy:

1
st

order phase transition

Transition temperature:

H

Gauge theory entropy:

λ

enhanced over naïve

large
-
N counting

phase transition

“small glitch in


extensive quantities”