Post on 16-Dec-2015
transcript
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
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]
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
= 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
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)]
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