1. 1 Holographic description of Hadrons from 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) /17

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

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

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

5. 5 D-brane open strings Gauge theory on the D-brane 4 dim String theory in a curved background replace D-branes with the corresponding curved background 10 dim “ Holographic dual ” dual! Why it works?

6. 6 How can we realize QCD in string theory? D8 D4 4 dim [Sakai-S.S. 2004] (low energy) QCD with massless quarks : gluon : quark S1S1 (1+4) dim D-brane (1+8) dim D-brane

7. 7 Holographic QCD D4 D4-brane on QCD with massless quarks (low energy) D8 + D8-D8 pairs Open + closed string theory in this background dual “ Holographic QCD ” String theory in the D4 background + D8-branes D8 replace D4 with curved background

8. 8 D4 QCD with massless quarks (low energy) Open + closed string theory in this background dual D8 (’t Hooft coupling) parameters : cut off scale string length string coupling good description for large low energy

9. 9 Do we have hadrons? Closed strings Open strings on D8 D4 wrapped on D4-brane D8-brane N c strings are attached glueballs mesons baryons Particles in this system

10. 10 Surprise : A lot of properties of hadrons can be extracted using this new description!

11. 11 Caution : We have only estimated the leading terms in the and expansions. is around 1 GeV. We should not expect too much. But, don’t be too pessimistic! Quark masses are neglected.

12. 12 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

13. 13 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. input [Sakai-S.S. 2004, 2005]

14. 14 1 st excited states 2 nd excited states [Imoto-Sakai-S.S. 2010] 3 rd excited states (See arXiv:1005.0655 for more details) Other mesons, including higher spin mesons, are obtained as excited string states. rotating open string higher spin meson

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

16. 16 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 GeV 2

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