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Holographic descriptionof

Hadronsfrom

String Theory

Shigeki Sugimoto (IPMU)

Rencontres de Moriond, March 25, 2011 @ La Thuile, Italy

(based on works with T.Sakai, H.Hata, S.Yamato, K. Hashimoto, T.Imoto, …)

(Review)

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Claim :

String theory can bea theory of hadrons

The string scale here is around 1 GeV.

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I’m NOT sayingQCD is wrong.

String theory (in a certain curved background)

QCDdual !

“ Holographic QCD ”

“Gauge/String duality”

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[Maldacena 1997,etc.]

Gauge theory

4 dim

String theoryin a curved background

10 dim“ Holographic dual ”

dual!

What is Gauge/String duality?

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D-braneopen strings

Gauge theoryon the D-brane

4 dim

String theory ina curved background

replace D-braneswith the corresponding curved background

10 dim“ Holographic dual ”

dual!

Why it works?

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How can we realizeQCD in string theory?

D8

D8D4

4 dim

[Sakai-S.S. 2004]

(low energy)

QCD with massless quarks

: gluon

: quark

S1

(1+4) dimD-brane

(1+8) dimD-brane

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Holographic QCD

D4

　 D4-brane on

QCD with massless quarks

(low energy)

D8

D8

+ D8-D8 pairs

Open + closed string theory in this backgrounddual

“ Holographic QCD ”

String theory in the D4 background

+ D8-branes

D8

replace D4with curvedbackground

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D4

QCD with massless quarks

(low energy)

Open + closed string theory in this backgrounddual

D8

D8

D8

(’t Hooft coupling)

parameters :

cut off scale string length

string coupling

good description for

large

large low energy

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Do we have hadrons?

Closed strings

Open strings on D8

D4 wrapped onD4-brane

D8-brane

Nc strings are attached

glueballs

mesons

baryons

Particles in this system

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Surprise :

A lot of properties ofhadrons can be extractedusing this new description!

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Caution :We have only estimated the leadingterms in the and expansions.

is around 1 GeV.

We should not expect too much.But, don’t be too pessimistic!

Quark masses are neglected.

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Meson effective theory is written asa 5 dim YM-CS theory in a curved background.

CS5-form

complete sets offunctions of

traditional meson effective action

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A lot of old models are reproduced withoutmaking 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 agreewith experimental data.

input

[Sakai-S.S. 2004, 2005]

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1st excited states

2nd excited states

[Imoto-Sakai-S.S. 2010]

3rd excited states

(See arXiv:1005.0655 for more details)

Other mesons, including higher spin mesons, are obtained as excited string states.

rotatingopen string

higher spinmeson

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Theory Experiment*) not established

*) *)

*)

mass

Baryon spectrum [Hata-Yamato-Sakai-S.S. 2007]

D-branesoliton in the 5dim theory＝

We can analyze the spectrum, magnetic moments,charge radii by quantizing this soliton cf) Skyrme model

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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 bea theory of hadrons

String theory (in a certain curved background)

meson baryon stringD-brane with Nc strings

D-brane

QCDdual !

“ Holographic QCD ”