Transcript ppt - Rencontres de Moriond

Holographic description
of
Hadrons
from
String Theory
(Review)
Shigeki Sugimoto (IPMU)
(based on works with T.Sakai, H.Hata, S.Yamato,
K. Hashimoto, T.Imoto, …)
Rencontres de Moriond, March 25, 2011 @ La Thuile, Italy
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Claim :
String theory can be
a theory of hadrons
The string scale here is around 1 GeV.
2
I’m NOT saying
QCD is wrong.
QCD
dual !
String theory
(in a certain curved background)
“ Holographic QCD ”
“Gauge/String duality”
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What is Gauge/String duality?
[Maldacena 1997,etc.]
Gauge theory
4 dim
dual!
String theory
in a curved background
10 dim
“ Holographic dual ”
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Why it works?
D-brane
open strings
replace D-branes
with the corresponding
curved background
Gauge theory
on the D-brane
4 dim
dual!
String theory in
a curved background
10 dim
“ Holographic dual ”
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How can we realize
QCD in string theory?
(1+4) dim
D-brane
[Sakai-S.S. 2004]
(1+8) dim
D-brane
S1
4 dim
: gluon
(low energy)
D8
D8
: quark
D4
with
QCD
massless quarks
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Holographic QCD
D4-brane on
+
replace D4
with curved
background
D8-D8 pairs
String theory in
the D4 background
+
D8-branes
D8
D8
D8
D4
(low energy)
with
QCD
massless quarks
dual
Open + closed string theory
in this background
“ Holographic QCD ” 7
D8
D8
D8
D4
(low energy)
with
QCD
massless quarks
parameters :
cut off scale
(’t Hooft coupling)
dual
Open + closed string theory
in this background
string coupling
string length
good description for
large
large
low energy 8
Do we have hadrons?
Particles in this system
Closed strings
glueballs
Open strings on D8
mesons
D8-brane
D4 wrapped on
baryons
D4-brane
Nc strings are attached
9
Surprise :
A lot of properties of
hadrons can be extracted
using this new description!
10
Caution :
We have only estimated the leading
terms in the
and
expansions.
is around 1 GeV.
Quark masses are neglected.
We should not expect too much.
But, don’t be too pessimistic!
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Meson effective theory is written as
a 5 dim
YM-CS theory in a curved background.
CS5-form
complete sets of
functions of
traditional meson effective action
12
A lot of old models are reproduced without
making any phenomenological assumptions!
Skyrme model
[Skyrme 1961]
Vector meson dominance
[Sakurai 1960, Gell-Mann-Zachriasen 1961]
Gell-Mann Sharp Wagner model [Gell-Mann –Sharpe-Wagner 1962]
Hidden local symmetry
[Bando-Kugo-Uehara-Yamawaki-Yanagida 1985]
masses and couplings roughly agree
with experimental data.
[Sakai-S.S. 2004, 2005]
input
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Other mesons, including higher spin mesons,
are obtained as excited string states.
[Imoto-Sakai-S.S. 2010]
rotating
open string
higher spin
meson
1st excited states
2nd excited states
3rd excited states
(See arXiv:1005.0655 for more details)
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Baryon spectrum
D-brane
[Hata-Yamato-Sakai-S.S. 2007]
＝ soliton in the 5dim theory
We can analyze the spectrum, magnetic moments,
charge radii by quantizing this soliton cf) Skyrme model
mass
Theory
Experiment
*)
*)
*) not established
*)
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Properties of nucleons
[Hashimoto-Sakai-S.S. 2008]
[See also,
Hong-Rho-Yee-Yi 2007,
Hata-Murata-Yamato 2008,
Kim-Zahed 2008]
nucleon ele-mag form factor
dipole （
experiment）
our result
GeV2
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Conclusion :
String theory can be
a theory of hadrons
dual !
QCD
String theory
(in a certain curved background)
“ Holographic QCD ”
D-brane
meson
baryon
string
D-brane with Nc strings
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