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1 Holographic description of Hadrons from String Theory Shigeki Sugimoto (IPMU) Rencontres de Moriond, March 25, La Thuile, Italy (based on works with T.Sakai, H.Hata, S.Yamato, K. Hashimoto, T.Imoto, …) (Review) /17

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

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

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

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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?

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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

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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

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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

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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

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

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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.

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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

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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]

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

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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

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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

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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 ”

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