Transcript Two Approaches to Holographic Nuclei

Two Approaches to Holographic Baryons/Nuclei
PILJIN YI
(KIAS)
5th APFB, Seoul, August 2011
Koji Hashimoto
Deog-Ki Hong
Norihiro Iizuka
Youngman Kim
Sangmin Lee
Jaemo Park
Mannque Rho
Ho-Ung Yee
Deokhyun Yi
1.
Holographic Chiral Lagrangian of Mesons and Baryons
2.
String Theory Origin
3.
D4’ ADHM Matrix Quantum Mechanics for Baryons
4.
Why ?
Maldacena 1997
1.
holography keeps color-singlets ( large N master fields ) only:
no trace of color indices remains in the D>4 holographic description
1.
holography keeps color-singlets ( large N master fields ) only:
no trace of color indices remains in the D>4 holographic description
 theory of glueballs, mesons, and baryons
gravitational theory
flavor gauge theory
flavor soliton/wrapped D-brane
1.
holography keeps color-singlets ( large N master fields ) only:
no trace of color indices remains in the D>4 holographic description
 theory of glueballs, mesons, and baryons
gravitational theory
flavor gauge theory
flavor soliton/wrapped D-brane
1. Holographic Chiral Lagrangian of Mesons and Baryons
Sakai-Sugimoto + Hong-Rho-Yee-Yi
Sakai, Sugimoto, 2004
Hong, Rho,Yee, P.Y., 2007
Sakai, Sugimoto, 2004
(i) pseudoscalars and spin1meson towers
packaged into a single 5D flavor gauge theory
mode-expand along the extra direction
classical coupling on N_f D8:
it dictates all couplings among
flavored physical states,
1.
holography keeps color-singlets ( large N master fields ) only :
no trace of color indices remains in the D>4 holographic description
2.
holography elevates a continuous global symmetry to a gauge symmetry
but in a D > 4 dimensional mathematical world :
4D flavor symmetry  5D flavor gauge theory
1.
holography keeps color-singlets ( large N master fields ) only :
no trace of color indices remains in the D>4 holographic description
2.
holography elevates a continuous global symmetry to a gauge symmetry
but in a D > 4 dimensional mathematical world :
4D quark number  5D Coulomb charge
baryon is a topological flavor soliton
Chern-Simons terms
 N quarks  single baryon
use the 5D instanton soliton as the 0th order configuration
minimize the 1st order energy to find
Hong, Rho, Yee,Yi, hep-th/0701276
Hata, Sakai, Sugimoto, Yamato, hep-th/0701280
baryon Compton size
<<
soliton size
<<
meson Compton sizes
 shape of the classical soliton is trustworthy, yet,
it can still be treated point-like for interaction with mesons
 isospin ½ spin ½ baryon field
 holographic chiral Lagrangian of baryon
coupled to mesons
Hong, Rho, Yee, P.Y., 2007
(ii) nucleons lifted to a single isospin ½ 5D spinor
5D minimal coupling
5D tensor coupling
the holographic origin of
1. the leading axial coupling to pions,
2. nucleon anomalous magnetic moments,
3. minimal couplings to axial vectors,
4. tensor couplings to vectors,
etc
leading in
leading in
nucleon predictions for nucleon-meson interactions
iso-singlet/triplet
(axial-)vector mesons
nucleon
quartic terms also present but not shown
Kim, Lee, P.Y. 2009
predictions for nucleon-meson interactions
all tensor couplings vanish identically,
except for those associated with
the tower of rho mesons (iso-triplet vectors)
(meaning that coefficients of the respective leading 1/ N behavior vanish,
and, thus, is NOT a consequence of large N countings)
Kim, Lee, P.Y. 2009
predictions for nucleon-meson interactions
nucleon
R. Machaleidt,
in Advances in Nuclear Physics, Vol. 19
Edited by J. W. Negele and E.Vogt
(Plenum, New York, 1986),
nucleon
Hong, Rho, Yee, P.Y., 2007
predictions for nucleon-meson interactions
nucleon
from 5D minimal term
from 5D tensor term
nucleon
Hoehler, Pietarinen, 1975
Stoks, Klomp, Terheggen, de Swart, 1994
Machleidt, 2001
Gross, Stadler, 2007
Hong, Rho, Yee, P.Y., 2007
predictions for nucleon-meson interactions
nucleon
?
pion
nucleon
Lee, Kim, P.Y., 2009
which leads to NN potential via one-boson exchange
Lee, Kim, P.Y., 2009
which leads to NN potential via one-boson exchange
NN repulsive core of solitonic baryon
4D baryon #
 5D Coulomb charge
 5D Coulomb repulsion
Kim, Zahed, 2009
Hashimoto, Sakai, Sugimoto, 2009
Lee, Kim, P.Y., 2009
NN repulsive core of solitonic baryon
Hashimoto, Sakai, Sugimoto, 2009
2. String Theory Origin
Witten 1998
IIA holographic QCD without flavor
D4
D4 : 0123 5
anti-periodic (=thermal)
boundary condition
for fermions !!!
Maldacena 1997
from IIA holographic QCD without flavor
D4
Sakai, Sugimoto, 2004
adding massless quarks
D8’
anti-D8’
D4
D4 : 0123 5
D8 : 01234 6789
anti-periodic (=thermal)
boundary condition
for fermions
massless quarks  bi-quark mesons
D8
anti-D8
D4
D8
away from the horizon
 Sakai-Sugimoto’s flavor gauge theory in 5D
alternate picture : baryons as wrapped D4-branes
D8
D4’
anti-D8
D4
D4 : 0123 5
D8 : 01234 6789
D4’ : 0
6789
alternate picture : baryons as wrapped D4-branes
D8
anti-D8
D4
D8’s
3. D4’ ADHM Matrix Quantum Mechanics for Baryons
Atiyah-Drinfeld-Hitchin-Manin
ADHM Matrix is equivalent to Topolgical Flavor Soliton Data
position data
D4’
size data
D4’
D8
ADHM Matrix is equivalent to Flavor Soliton Data
D4’
diagonalize along a,b indices
D4’
D8
position of a-th baryon
stringy regime
naïve region of validity for
ADHM matrix model
gravity + gauge theory regime
naïve region of validity for
the flavor soliton picture
baryon dynamics  susy broken ADHM Quantum Mechanics
Hashimoto, Iizuka, P.Y. 2010
baryon dynamics  susy broken ADHM Quantum Mechanics
Hashimoto, Iizuka, P.Y. 2010
4. Why ?
is the the two pictures of baryons compatible with each other ?
if so, why ?
can we profit from the dual pictures ?
size of a single baryon, again, in ADHM Matrix QM ?
size of a single baryon, again, in ADHM Matrix QM ?
size of a single baryon, again, in ADHM Matrix QM ?
minimizing the approximate energy functional
Hashimoto, Iizuka, P.Y. 2010
NN repulsive core, again, in ADHM Matrix QM
NN repulsive core, again, in ADHM Matrix QM
NN repulsive core, again, in ADHM Matrix QM
NN repulsive core, again, in ADHM Matrix QM
Hashimoto, Iizuka, P.Y, 2010
baryon size comparison
baryon size comparison
baryon size comparison
if we take
as ADHM/Instanton equivalence would suggest
NN-repulsive-core comparison
NN-repulsive-core comparison
so again, modulo numerical factor 5/4, the two approaches to baryons gives
the same answer for short distance repulsive core
stringy regime
naïve region of validity for
ADHM matrix model
gravity + gauge theory regime
naïve region of validity for
the flavor soliton picture
stringy regime
susy-protected region of validity for
ADHM matrix model
gravity + gauge theory regime
naïve region of validity for
the flavor soliton picture
NN, NNN, NNNN, ……
for NN, iso-singlet attractive channel exists at 1-loop,
while missing in the flavor soliton picture
k-body interaction becomes k x k
nearly supersymmetric quantum mechanics
effects of glue sector missed by flavor solitons ?
summary & ……
1.
chiral theory of infinite varieties of mesons and solitonic
baryons in closed form
(infinitely predictive, reasonable predictions for some
low energy processes, vector dominance for E&M, …)
2.
ADHM Matrix QM emulates short distance behaviors of
Flavor Solitons remarkably well, and is more scalable for large k
3.
emergent supersymmetry in holographic description ?
4.
a model of multi-nucleon system based on Matrix description ?