1. 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

2. 1.Holographic Chiral Lagrangian of Mesons and Baryons 2.String Theory Origin 3.D4’ ADHM Matrix Quantum Mechanics for Baryons 4.Why ?

3. 1.holography keeps color-singlets ( large N master fields ) only: no trace of color indices remains in the D>4 holographic description Maldacena 1997

4. 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

5. 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

6. 1. Holographic Chiral Lagrangian of Mesons and Baryons Sakai-Sugimoto + Hong-Rho-Yee-Yi

7. Hong, Rho, Yee, P.Y., 2007 Sakai, Sugimoto, 2004

8. (i) pseudoscalars and spin1meson towers packaged into a single 5D flavor gauge theory Sakai, Sugimoto, 2004

9. mode-expand along the extra direction

10. classical coupling on N_f D8: it dictates all couplings among flavored physical states,

11. 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

12. 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

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

14. 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

15. 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

16. 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

17. leading in

19. nucleon iso-singlet/triplet (axial-)vector mesons quartic terms also present but not shown predictions for nucleon-meson interactions

20. 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

21. 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

22. 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

23. nucleon pion nucleon ? predictions for nucleon-meson interactions Hong, Rho, Yee, P.Y., 2007

24. which leads to NN potential via one-boson exchange Lee, Kim, P.Y., 2009

25. which leads to NN potential via one-boson exchange Lee, Kim, P.Y., 2009

26. 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

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

28. 2. String Theory Origin

29. D4 : 0123 5 IIA holographic QCD without flavor Witten 1998 anti-periodic (=thermal) boundary condition for fermions !!! D4

30. from IIA holographic QCD without flavor Maldacena 1997

31. adding massless quarks D4 : 0123 5 D8 : 01234 6789 anti-periodic (=thermal) boundary condition for fermions D8’ anti-D8’ D4 Sakai, Sugimoto, 2004

32. massless quarks  bi-quark mesons D8 D4 D8 anti-D8

33. away from the horizon  Sakai-Sugimoto’s flavor gauge theory in 5D

34. alternate picture : baryons as wrapped D4-branes D4 : 0123 5 D8 : 01234 6789 D4’ : 0 6789 D8 anti-D8 D4’ D4

35. D8’s D4 D8 anti-D8 alternate picture : baryons as wrapped D4-branes

36. 3. D4’ ADHM Matrix Quantum Mechanics for Baryons

37. ADHM Matrix is equivalent to Topolgical Flavor Soliton Data size data position data D8 D4’ Atiyah-Drinfeld-Hitchin-Manin

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

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

40. baryon dynamics  susy broken ADHM Quantum Mechanics Hashimoto, Iizuka, P.Y. 2010

41. baryon dynamics  susy broken ADHM Quantum Mechanics

42. 4. Why ? is the the two pictures of baryons compatible with each other ? if so, why ? can we profit from the dual pictures ?

43. size of a single baryon, again, in ADHM Matrix QM ?

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

46. NN repulsive core, again, in ADHM Matrix QM

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

50. baryon size comparison

52. if we take as ADHM/Instanton equivalence would suggest

53. NN-repulsive-core comparison

54. so again, modulo numerical factor 5/4, the two approaches to baryons gives the same answer for short distance repulsive core

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

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

57. 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 ?

58. 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 ?