Nuclear Forces from String Theory Koji Hashimoto (RIKEN, Mathematical physics lab) 22 nd July arXiv/ N.Iizuka, P.Yi, KH arXiv/ , KH arXiv/ N.Iizuka, KH arXiv/ T.Sakai, S.Sugimoto, KH arXiv/ N.Iizuka, T.Nakatsukasa, KH

Superstring may not be useless

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

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

Mesons : Spectra, interactions, Skyrme term, Vector meson dominance, Hidden local symmetry, Chiral perturbations, Quark mass effects, … What can superstring compute? Baryons : Spectra, interactions, nuclear forces, 3-body nuclear forces, Giant resonances, … Exotics : Glueball spectra, Glueball decays, … General : Chiral condensate, Quark antiquark forces, Wilson / Polyakov loop, Phase diagram, Gluon scattering, … 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 N c, “QCD” with junk massive fields

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

Holographic QCD : two physics connected Large N c “QCD” Superstring Meson sector Glueball sector Supergravity in 10d curved spacetime Flavor U(N f ) Yang-Mills in higher dim. BaryonD-brane in 10d spacetime QCD string Fundamental string in curved space Chiral sym.breakingHiggsing Flavor gauge symmetries Finite temperatureHawking temperature DeconfinementEvent horizon of Black hole Dense matterElectric field on Flavor U(N f ) Color superconductorD-brane melting

SuperstringExperiment Couplings, Radii of Nucleon Lattice [Sakai,Sugimoto,KH ( )] (0.74 fm) fm 2.2 – –1.9 (0.875 fm) 2 – fm fm 2.79 – – – 7.5 – –2.45

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

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

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

Plan Nuclear matrix model Holography Phase diagram

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

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

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

Plan Nuclear matrix model Holography Phase diagram

= Source of closed strings = Source of gravity = Extended blackhole “blackbrane” in 10D 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 Deform Open string theory on the Dp-brane is : SU(Nc) gauge theory in p+1 dimensions Nc open strings Nc parallel Dp-branes 2

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

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

Baryon D-brane Holography : Baryon  D-brane

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

Black hole Holography : Heavy Nucleus  Black hole Heavy Nucleus

Plan Nuclear matrix model Holography Phase diagram

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

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

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

Color superconductor in N=2 Super QCD ? Quarks are accompanied by Squarks  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) [Chen, Matsuura, KH (09)]

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

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

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)]

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