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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

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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 theoryflavor 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 theoryflavor 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 among flavored 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 0 th order configuration minimize the 1 st 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 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

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leading in

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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 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

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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

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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, 2009 Hashimoto, Sakai, Sugimoto, 2009 Lee, 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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from IIA holographic QCD without flavor Maldacena 1997

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adding massless quarks D4 : 0123 5 D8 : 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-D8 D4’ 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’ Atiyah-Drinfeld-Hitchin-Manin

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

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

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baryon size comparison

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if we take as ADHM/Instanton equivalence would suggest

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NN-repulsive-core comparison

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

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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 ?

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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 ?

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