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 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 ?

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 theoryflavor 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 theoryflavor 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 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

Chern-Simons terms  N quarks  single baryon baryon is a topological flavor soliton

Hong, Rho, Yee, Yi, hep-th/ Hata, Sakai, Sugimoto, Yamato, hep-th/ use the 5D instanton soliton as the 0 th order configuration minimize the 1 st 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 coupling5D 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 in

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 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), predictions for nucleon-meson interactions Kim, Lee, P.Y. 2009

from 5D minimal term from 5D tensor term nucleon Hoehler, Pietarinen, 1975 Stoks, Klomp, Terheggen, de Swart, 1994 Machleidt, 2001 Gross, 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, 2009 Hashimoto, Sakai, Sugimoto, 2009 Lee, Kim, P.Y., D baryon #  5D Coulomb charge  5D Coulomb repulsion

NN repulsive core of solitonic baryon Hashimoto, Sakai, Sugimoto, 2009

2. String Theory Origin

D4 : IIA holographic QCD without flavor Witten 1998 anti-periodic (=thermal) boundary condition for fermions !!! D4

from IIA holographic QCD without flavor Maldacena 1997

adding massless quarks D4 : D8 : 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 : D8 : D4’ : D8 anti-D8 D4’ 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’ Atiyah-Drinfeld-Hitchin-Manin

ADHM Matrix is equivalent to Flavor Soliton Data D8 D4’ diagonalize along a,b indices position of a-th baryon

stringy regimegravity + 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

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 ?

minimizing the approximate energy functional Hashimoto, Iizuka, P.Y. 2010

NN repulsive core, again, in ADHM Matrix QM

Hashimoto, Iizuka, P.Y, 2010 NN repulsive core, again, in ADHM Matrix QM

baryon size comparison

if we take as ADHM/Instanton equivalence would suggest

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 regimegravity + gauge theory regime naïve region of validity for the flavor soliton picture naïve region of validity for ADHM matrix model

stringy regimegravity + 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 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 ?