two approaches to holographic baryons/nuclei piljin yi (kias) 5 th apfb, seoul, august 2011 koji...
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Two Approaches to Holographic Baryons/Nuclei
PILJIN YI(KIAS)
5th APFB, Seoul, August 2011Koji Hashimoto
Deog-Ki HongNorihiro Iizuka
Youngman KimSangmin Lee
Jaemo ParkMannque Rho
Ho-Ung YeeDeokhyun Yi
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1. Holographic Chiral Lagrangian of Mesons and Baryons
2. String Theory Origin
3. D4’ ADHM Matrix Quantum Mechanics for Baryons
4. Why ?
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1. holography keeps color-singlets ( large N master fields ) only: no trace of color indices remains in the D>4 holographic description
Maldacena 1997
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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 theoryflavor soliton/wrapped D-brane
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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 theoryflavor soliton/wrapped D-brane
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1. Holographic Chiral Lagrangian of Mesons and Baryons
Sakai-Sugimoto + Hong-Rho-Yee-Yi
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Hong, Rho, Yee, P.Y., 2007
Sakai, Sugimoto, 2004
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(i) pseudoscalars and spin1meson towers packaged into a single 5D flavor gauge theory
Sakai, Sugimoto, 2004
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mode-expand along the extra direction
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classical coupling on N_f D8:it dictates all couplings amongflavored physical states,
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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
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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
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Chern-Simons terms
N quarks single baryon
baryon is a topological flavor soliton
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Hong, Rho, Yee, Yi, hep-th/0701276 Hata, Sakai, Sugimoto, Yamato, hep-th/0701280
use the 5D instanton soliton as the 0th order configuration
minimize the 1st order energy to find
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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
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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
(ii) nucleons lifted to a single isospin ½ 5D spinor
Hong, Rho, Yee, P.Y., 2007
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leading inleading in
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nucleon
nucleon
iso-singlet/triplet(axial-)vector mesons
quartic terms also present but not shown
predictions for nucleon-meson interactions
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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
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nucleon
nucleon
R. Machaleidt, in Advances in Nuclear Physics, Vol. 19Edited by J. W. Negele and E. Vogt (Plenum, New York, 1986),
predictions for nucleon-meson interactions
Kim, Lee, P.Y. 2009
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from 5D minimal term
from 5D tensor term
nucleon
nucleon
Hoehler, Pietarinen, 1975Stoks, Klomp, Terheggen, de Swart, 1994Machleidt, 2001Gross, Stadler, 2007
predictions for nucleon-meson interactions
Hong, Rho, Yee, P.Y., 2007
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nucleon
pion
nucleon
?
predictions for nucleon-meson interactions
Hong, Rho, Yee, P.Y., 2007
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which leads to NN potential via one-boson exchange
Lee, Kim, P.Y., 2009
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which leads to NN potential via one-boson exchange
Lee, Kim, P.Y., 2009
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NN repulsive core of solitonic baryon
Kim, Zahed, 2009Hashimoto, Sakai, Sugimoto, 2009Lee, Kim, P.Y., 2009
4D baryon #
5D Coulomb charge 5D Coulomb repulsion
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NN repulsive core of solitonic baryon
Hashimoto, Sakai, Sugimoto, 2009
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2. String Theory Origin
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D4 : 0123 5
IIA holographic QCD without flavor
Witten 1998
anti-periodic (=thermal)boundary condition for fermions !!!
D4
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D4
from IIA holographic QCD without flavor
Maldacena 1997
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adding massless quarks
D4 : 0123 5D8 : 01234 6789
anti-periodic (=thermal)boundary condition for fermions
D8’
anti-D8’
D4
Sakai, Sugimoto, 2004
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massless quarks bi-quark mesons
D8
D4
D8
anti-D8
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away from the horizon
Sakai-Sugimoto’s flavor gauge theory in 5D
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alternate picture : baryons as wrapped D4-branes
D4 : 0123 5 D8 : 01234 6789
D4’ : 0 6789
D8
anti-D8D4’
D4
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D8’s
D4
D8
anti-D8
alternate picture : baryons as wrapped D4-branes
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3. D4’ ADHM Matrix Quantum Mechanics for Baryons
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ADHM Matrix is equivalent to Topolgical Flavor Soliton Data
size data
position data
D8
D4’
D4’
Atiyah-Drinfeld-Hitchin-Manin
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ADHM Matrix is equivalent to Flavor Soliton Data
D8
D4’
D4’
diagonalize along a,b indices
position of a-th baryon
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stringy regime gravity + gauge theory regime
naïve region of validity for the flavor soliton picture
naïve region of validity for ADHM matrix model
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baryon dynamics susy broken ADHM Quantum Mechanics
Hashimoto, Iizuka, P.Y. 2010
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Hashimoto, Iizuka, P.Y. 2010
baryon dynamics susy broken ADHM Quantum Mechanics
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4. Why ?
is the the two pictures of baryons compatible with each other ?
if so, why ?
can we profit from the dual pictures ?
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size of a single baryon, again, in ADHM Matrix QM ?
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size of a single baryon, again, in ADHM Matrix QM ?
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size of a single baryon, again, in ADHM Matrix QM ?
minimizing the approximate energy functional
Hashimoto, Iizuka, P.Y. 2010
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NN repulsive core, again, in ADHM Matrix QM
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NN repulsive core, again, in ADHM Matrix QM
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NN repulsive core, again, in ADHM Matrix QM
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Hashimoto, Iizuka, P.Y, 2010
NN repulsive core, again, in ADHM Matrix QM
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baryon size comparison
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baryon size comparison
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baryon size comparison
if we take as ADHM/Instanton equivalence would suggest
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NN-repulsive-core comparison
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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
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stringy regime gravity + gauge theory regime
naïve region of validity for the flavor soliton picture
naïve region of validity for ADHM matrix model
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stringy regime gravity + gauge theory regime
naïve region of validity for the flavor soliton picture
susy-protected region of validity for ADHM matrix model
![Page 57: Two Approaches to Holographic Baryons/Nuclei PILJIN YI (KIAS) 5 th APFB, Seoul, August 2011 Koji Hashimoto Deog-Ki Hong Norihiro Iizuka Youngman Kim Sangmin](https://reader035.vdocuments.site/reader035/viewer/2022062712/56649c775503460f9492bf2f/html5/thumbnails/57.jpg)
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 knearly supersymmetric quantum mechanics
effects of glue sector missed by flavor solitons ?
![Page 58: Two Approaches to Holographic Baryons/Nuclei PILJIN YI (KIAS) 5 th APFB, Seoul, August 2011 Koji Hashimoto Deog-Ki Hong Norihiro Iizuka Youngman Kim Sangmin](https://reader035.vdocuments.site/reader035/viewer/2022062712/56649c775503460f9492bf2f/html5/thumbnails/58.jpg)
summary & ……
1. chiral theory of infinite varieties of mesons and solitonic baryons in closed form (infinitely predictive, reasonable predictions for somelow 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 ?