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

1. Holographic Chiral Lagrangian of Mesons and Baryons

2. String Theory Origin

3. D4’ ADHM Matrix Quantum Mechanics for Baryons

4. Why ?

1. holography keeps color-singlets ( large N master fields ) only: no trace of color indices remains in the D>4 holographic description

Maldacena 1997

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

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

1. Holographic Chiral Lagrangian of Mesons and Baryons

Sakai-Sugimoto + Hong-Rho-Yee-Yi

Hong, Rho, Yee, P.Y., 2007

Sakai, Sugimoto, 2004

(i) pseudoscalars and spin1meson towers packaged into a single 5D flavor gauge theory

Sakai, Sugimoto, 2004

mode-expand along the extra direction

classical coupling on N_f D8:it dictates all couplings amongflavored 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

Chern-Simons terms

N quarks single baryon

baryon is a topological flavor soliton

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

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

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

leading inleading in

nucleon

nucleon

iso-singlet/triplet(axial-)vector mesons

quartic terms also present but not shown

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

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

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

nucleon

pion

nucleon

?

predictions for nucleon-meson interactions

Hong, Rho, Yee, P.Y., 2007

which leads to NN potential via one-boson exchange

Lee, Kim, P.Y., 2009

which leads to NN potential via one-boson exchange

Lee, Kim, P.Y., 2009

NN repulsive core of solitonic baryon

Kim, Zahed, 2009Hashimoto, Sakai, Sugimoto, 2009Lee, Kim, P.Y., 2009

4D baryon #

5D Coulomb charge 5D Coulomb repulsion

NN repulsive core of solitonic baryon

Hashimoto, Sakai, Sugimoto, 2009

2. String Theory Origin

D4 : 0123 5

IIA holographic QCD without flavor

Witten 1998

anti-periodic (=thermal)boundary condition for fermions !!!

D4

D4

from IIA holographic QCD without flavor

Maldacena 1997

adding massless quarks

D4 : 0123 5D8 : 01234 6789

anti-periodic (=thermal)boundary condition for fermions

D8’

anti-D8’

D4

Sakai, Sugimoto, 2004

massless quarks bi-quark mesons

D8

D4

D8

anti-D8

away from the horizon

Sakai-Sugimoto’s flavor gauge theory in 5D

alternate picture : baryons as wrapped D4-branes

D4 : 0123 5 D8 : 01234 6789

D4’ : 0 6789

D8

anti-D8D4’

D4

D8’s

D4

D8

anti-D8

alternate picture : baryons as wrapped D4-branes

3. D4’ ADHM Matrix Quantum Mechanics for Baryons

ADHM Matrix is equivalent to Topolgical Flavor Soliton Data

size data

position data

D8

D4’

D4’

Atiyah-Drinfeld-Hitchin-Manin

ADHM Matrix is equivalent to Flavor Soliton Data

D8

D4’

D4’

diagonalize along a,b indices

position of a-th baryon

stringy regime gravity + gauge theory regime

naïve region of validity for the flavor soliton picture

naïve region of validity for ADHM matrix model

baryon dynamics susy broken ADHM Quantum Mechanics

Hashimoto, Iizuka, P.Y. 2010

Hashimoto, Iizuka, P.Y. 2010

baryon dynamics susy broken ADHM Quantum Mechanics

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

Hashimoto, Iizuka, P.Y, 2010

NN repulsive core, again, in ADHM Matrix QM

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 gravity + gauge theory regime

naïve region of validity for the flavor soliton picture

naïve region of validity for ADHM matrix model

stringy regime gravity + gauge theory regime

naïve region of validity for the flavor soliton picture

susy-protected region of validity for ADHM matrix model

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 ?

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 ?