Nuclear Forces from String Theory

　 Koji Hashimoto (RIKEN, Mathematical physics lab)

22nd July 2010 @ECT*

arXiv/1003.4988 N.Iizuka, P.Yi, KH

arXiv/0809.3141,0910.2303 KHarXiv/1005.4412 N.Iizuka, KH

arXiv/0901.4449 T.Sakai, S.Sugimoto, KH

arXiv/0911.1035 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 ModelProper 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 Nc, “QCD” with junk massive fields

Caveat

QCD SU(Nc) QCD + extra massive matter

2 parametersgeneralize1 parameter

Superstringmathematics

Hadronic theory

Large Nc

+ 1/Nccorrections

Large Nc hadronic theory

1) 2 parameters : QCD coupling and QCD scale2) Large Nc expansion

Holographic QCD : two physics connected

Large Nc “QCD” Superstring

Meson sector

Glueball sector Supergravity in 10d curved spacetime

Flavor U(Nf ) Yang-Mills in higher dim.

Baryon D-brane in 10d spacetime

QCD string Fundamental string in curved space

Chiral sym.breaking Higgsing Flavor gauge symmetries

Finite temperature Hawking temperature

Deconfinement Event horizon of Black hole

Dense matter Electric field on Flavor U(Nf )

Color superconductor D-brane melting

Superstring Experiment

Couplings, Radii of Nucleon

Lattice

[Sakai,Sugimoto,KH (0806.3122)]

(0.74 fm)2

00.54 fm

2.2– 1.30.737.55.84.42.3

0.20–1.9

(0.875 fm)2

– 0.116 fm2

0.674 fm2.79

–1.911.2713.2

4.2 – 6.53.7 – 7.5

–––

4.992.490.06

–2.45

Nucleon Form factor

Superstring :

Experiment (empirically known dipole behavior)

[Sakai,Sugimoto,KH 0806.3122]

Nucleon mass vs. Quark mass

higher.

Superstring :

[Hirayama,Hong,KH, 0906.0402]

Lattice :

Hyperon Spectra

Our inputs :

Mass splitting of baryons with

Mass splitting of baryons with

Superstring

Superstring

Superstring

Superstring

[Iizuka,Ishii,Kadoh,KH, 0910.1179]

0.5 1 1.5 2

0.2

0.4

0.6

0.8

1

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 1003.4988]

Nuclearphysics

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/r2

[Iizuka,Yi, KH 1003.4988][Iizuka, S.Aoki, KH, in progress]

p

n

A=3 : 3-body nuclear force

p nHe-3

nucleus

n n Neutronstar

spin : averaged All positive

[Iizuka, KH,1005.4412][Iizuka, Nakatsukasa, KH, 0911.1035]

Large A : Giant resonances[KH (0809.3141,0910.2303)]

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 fieldClosed 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

Blackbrane

Nc D-branes

Propagation of SU(Nc) gauge theory

composite states

Propagation of gravitonin near-horizon geometry

of black p-brane

(Glueball)

Gluon

Large NcLarge λ

Nf “flavor D-brane”

Propagation of meson U(Nf) gauge fields in higher dim. D-braneon curved background

Quark

Holography : Meson Gauge boson in 10 dim

BaryonD-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 (0205236)]

No running of gauge coupling(conformal, strongly coupled)

Gluons: deconfinedDiscrete meson states

Chemical potential and phase transition

Chemical potential = asymptotic value of on D7.

Flat Spike

Temperature = Hawking temperature of Black hole

Gluon : deconfinedMeson : discrete

Gluon : deconfinedMeson : 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

D3D7 YM

instanton

Dissolution of D3 into D7 = YM instanton = Squark condensation (Higgs phase)

[Chen, Matsuura, KH (09)]

Three phases of N=2 Super QCD

D3size

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 ModelProper limit

Nuclear force, phase diagram

Solve QCD : difficult

Various aspects of QCD : necessity to map whole QCD to effective description