Holographic description of Hadrons from String Theory Review

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 1 /17

Claim : String theory can be a theory of hadrons The string scale here is around 1 Ge. V. 2

I’m NOT saying QCD is wrong. QCD dual ! String theory (in a certain curved background) “ Holographic QCD ” “Gauge/String duality” 3

What is Gauge/String duality? [Maldacena 1997, etc. ] Gauge theory 4 dim dual! String theory in a curved background 10 dim “ Holographic dual ” 4

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 ” 5

How can we realize QCD in string theory? (1+4) dim D-brane (1+8) dim D-brane S 1 4 dim : gluon (low energy) D 8 [Sakai-S. S. 2004] : quark D 4 with QCD massless quarks 6

Holographic QCD 　 D 4 -brane on + replace D 4 with curved background D 8 -D 8 pairs String theory in the D 4 background + D 8 -branes D 8 D 8 D 4 (low energy) with QCD massless quarks dual Open + closed string theory in this background “ Holographic QCD ” 7

D 8 D 8 D 4 (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 low energy 8

Do we have hadrons? Particles in this system Closed strings glueballs Open strings on D 8 mesons D 8 -brane D 4 wrapped on baryons D 4 -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 Ge. V. Quark masses are neglected. We should not expect too much. But, don’t be too pessimistic! 11

Meson effective theory is written as a 5 dim YM-CS theory in a curved background. CS 5 -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 13

Other mesons, including higher spin mesons, are obtained as excited string states. [Imoto-Sakai-S. S. 2010] rotating open string higher spin meson 1 st excited states 2 nd excited states 3 rd excited states (See ar. Xiv: 1005. 0655 for more details) 14

Baryon spectrum D-brane [Hata-Yamato-Sakai-S. S. 2007] ＝ soliton in the 5 dim theory We can analyze the spectrum, magnetic moments, charge radii by quantizing this soliton cf) Skyrme model mass Theory Experiment *) *) *) not established *) 15

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 Ge. V 2 16

Conclusion : String theory can be a theory of hadrons QCD dual ! String theory (in a certain curved background) “ Holographic QCD ” D-brane meson baryon string D-brane with Nc strings 17