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Nuclear Forces from String Theory

22 nd July 2010 @ECT*. Nuclear Forces from String Theory. Koji Hashimoto (RIKEN, Mathematical physics lab). arXiv/1003.4988 N.Iizuka, P.Yi, KH. arXiv/1005.4412 N.Iizuka, KH. arXiv/0809.3141,0910.2303 KH. arXiv/0901.4449 T.Sakai, S.Sugimoto, KH.

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Nuclear Forces from String Theory

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  1. 22nd July 2010 @ECT* Nuclear Forces from String Theory Koji Hashimoto (RIKEN, Mathematical physics lab) arXiv/1003.4988 N.Iizuka, P.Yi, KH arXiv/1005.4412 N.Iizuka, KH arXiv/0809.3141,0910.2303 KH arXiv/0901.4449 T.Sakai, S.Sugimoto, KH arXiv/0911.1035 N.Iizuka, T.Nakatsukasa, KH

  2. Superstring may not be useless

  3. M(atrix) theory [Banks, Fischler, Shenker, Susskind (1996)] Nuclear matrix model [Iizuka, Yi, KH (2010)]

  4. Problem Solve QCD : difficult String theory is useless Cause Interesting aspects of QCD lie at strong coupling region Various aspects of QCD : necessity to map whole QCD to effective description Our solution QCD + Superstring mathematics (“holography”) Higher dimensional gravity + gauge, Nuclear Matrix Model Proper limit Nuclear force, phase diagram

  5. What can superstring compute? General : Chiral condensate, Quark antiquark forces, Wilson / Polyakov loop, Phase diagram, Gluon scattering, … Mesons : Spectra, interactions, Skyrme term, Vector meson dominance, Hidden local symmetry, Chiral perturbations, Quark mass effects, … Baryons : Spectra, interactions, nuclear forces, 3-body nuclear forces, Giant resonances, … Exotics : Glueball spectra, Glueball decays, … Hot QCD : Deconfinement transition, Chiral restoration, Quark gluon plasma, Viscosity, Jet quenching parameters, Quark drag force, meson melting and decay width, … Dense QCD : Chiral restoration, Color superconductor, Meson mass in nuclear matter, … Caveat : Large Nc, “QCD” with junk massive fields

  6. Caveat SU(Nc) QCD + extra massive matter QCD 1 parameter 2 parameters generalize Superstring mathematics Large Nc + 1/Nc corrections Large Nc hadronic theory Hadronic theory 1) 2 parameters : QCD coupling and QCD scale 2) Large Nc expansion

  7. Holographic QCD : two physics connected Superstring Large Nc “QCD” Glueball sector Supergravity in 10d curved spacetime Meson sector Flavor U(Nf ) Yang-Mills in higher dim. Baryon D-brane in 10d spacetime QCD string Fundamental string in curved space Deconfinement Event horizon of Black hole Finite temperature Hawking temperature Chiral sym.breaking Higgsing Flavor gauge symmetries Dense matter Electric field on Flavor U(Nf ) Color superconductor D-brane melting

  8. Couplings, Radii of Nucleon [Sakai,Sugimoto,KH (0806.3122)] Superstring Experiment (0.74 fm)2 0 0.54 fm 2.2 – 1.3 0.73 7.5 5.8 4.4 2.3 0.20 –1.9 (0.875 fm)2 – 0.116 fm2 0.674 fm 2.79 –1.91 1.27 13.2 4.2 – 6.5 3.7 – 7.5 – – – Lattice 4.99 2.49 0.06 –2.45

  9. Nucleon Form factor Experiment (empirically known dipole behavior) [Sakai,Sugimoto,KH 0806.3122] Superstring : Nucleon mass vs. Quark mass higher. [Hirayama,Hong,KH, 0906.0402] Superstring : Lattice :

  10. Hyperon Spectra [Iizuka,Ishii,Kadoh,KH, 0910.1179] Mass splitting of baryons with Superstring Superstring Mass splitting of baryons with Superstring Superstring Our inputs :

  11. Meson mass in dense matter [Ishii,KH (in progress)] Superstring : -6%

  12. Plan Nuclear matrix model Holography Phase diagram

  13. Superstring derives multi-nucleon system Nuclear physics “Nuclear Matrix Model” : Multi-Baryons at short distances [Iizuka,Yi, KH 1003.4988] : A x A Hermitian matrix Eigenvalues of  location of A baryons Only two parameters : ,

  14. A=1 : Baryon spectrum Hamiltonian spectrum : 940+,1359+,1359-,1778+,1778-,… :inputs Exp. : 940+,1440+,1535-,1710+,1655-,… A=2 : Nuclear force, repulsive core [Iizuka,Yi, KH 1003.4988] [Iizuka, S.Aoki, KH, in progress] Repulsive core, Universal (even for 3 flavors), Scaling : 1/r2

  15. A=3 : 3-body nuclear force [Iizuka, KH,1005.4412] [Iizuka, Nakatsukasa, KH, 0911.1035] He-3 nucleus p n p Neutron star n n n spin : averaged All positive Large A : Giant resonances [KH (0809.3141,0910.2303)] Pb nucleus Cross- section Giant Resonance Exp.: Excitation energy Reproducing A dependence

  16. Plan Nuclear matrix model Holography Phase diagram

  17. Deform Why? D-branes giving the tool Quantizing strings defined in 10D spacetime Open string Massless gauge field Closed string Massless graviton D-branes = Object on which open strings can end Nc parallel Dp-branes = Source of closed strings = Source of gravity = Extended blackhole “blackbrane” in 10D Open string theory on the Dp-brane is : SU(Nc) gauge theory in p+1 dimensions 2 Nc open strings

  18. Holography : Glueball  Gravity Black brane Nc D-branes Gluon Propagation of SU(Nc) gauge theory composite states Propagation of graviton in near-horizon geometry of black p-brane Large Nc Large λ (Glueball)

  19. Holography : Meson  Gauge boson in 10 dim Nf “flavor D-brane” Quark U(Nf) gauge fields in higher dim. D-brane on curved background Propagation of meson

  20. Holography : Baryon  D-brane Baryon D-brane

  21. Holography : Multi Nucleon  Matrix A x A matrix model A nucleons = Nucleus

  22. Holography : Heavy Nucleus  Black hole Black hole Heavy Nucleus

  23. Plan Nuclear matrix model Holography Phase diagram

  24. Nf D7 Nc D3 Toy model of QCD : N=2 Super QCD D3-D7 model [Karch, Katz (0205236)] distance ~ quark mass Gluons: deconfined Discrete meson states No running of gauge coupling (conformal, strongly coupled)

  25. Chemical potential and phase transition Chemical potential = asymptotic value of on D7. Temperature = Hawking temperature of Black hole Two solutions for the D7 shape Spike Flat Gluon : deconfined Meson : discrete Gluon : deconfined Meson : continuous

  26. QGP Hadron Phase diagram of N=2 super QCD Spiky shape is favored for large High density, Color superconductor? [Kobayashi,Mateos,Matsuura,Myers,Thomson (06)] [Karch,O’Bannon(07)] [Nakamura,Seo,Sin,Yogendran (07)] [Gohroku,Ishihara,Nakamura(07)]

  27. Color superconductor in N=2 Super QCD ? Quarks are accompanied by Squarks [Chen, Matsuura, KH (09)] • When baryon chemical potential is turned on, the squarks get condensed first!  Color-Flavor Locking, Higgs phase D3 D7 YM instanton Dissolution of D3 into D7 = YM instanton = Squark condensation (Higgs phase)

  28. Three phases of N=2 Super QCD E D3 size Low T High T

  29. Phase diagram of N=2 Super QCD [Chen, Matsuura, KH (09)] QGP Color-Flavor locking (Higgs) Hadron

  30. Phase diagram of non-SUSY large Nc QCD QGP ? Color-Flavor locking (Higgs) Hadron [Aharony,Sonnenschein,Yankielowicz(06)] [Kim, Sin, Zahed(06)] [Horigome,Tanii(06)] [Bergman, Lifschytz, Lippert (07)] [Chuang, Dai, Kawamoto, Lin, Yeh (2010)]

  31. Problem Solve QCD : difficult String theory is useless Cause Interesting aspects of QCD lie at strong coupling region Various aspects of QCD : necessity to map whole QCD to effective description Our solution QCD + Superstring mathematics (“holography”) Higher dimensional gravity + gauge, Nuclear Matrix Model Proper limit Nuclear force, phase diagram

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