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Two Approaches to Holographic Baryons/Nuclei PILJIN YI (KIAS) 5 th APFB, Seoul, August 2011

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. Holographic Chiral Lagrangian of Mesons and Baryons String Theory Origin

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Two Approaches to Holographic Baryons/Nuclei PILJIN YI (KIAS) 5 th APFB, Seoul, August 2011

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  1. Two Approaches to Holographic Baryons/NucleiPILJIN YI(KIAS)5th 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. Holographic Chiral Lagrangian of Mesons and Baryons • String Theory Origin • D4’ ADHM Matrix Quantum Mechanics for Baryons • Why ?

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

  4. 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 theory flavor soliton/wrapped D-brane

  5. 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 theory flavor soliton/wrapped D-brane

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

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

  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 amongflavored physical states,

  11. 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. holography keeps color-singlets ( large N master fields ) only : no trace of color indices remains in the D>4 holographic description • 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. baryon is a topological flavor soliton Chern-Simons terms  N quarks  single baryon

  14. use the 5D instanton soliton as the 0th order configuration minimize the 1st order energy to find Hong, Rho, Yee, Yi, hep-th/0701276 Hata, Sakai, Sugimoto, Yamato, hep-th/0701280

  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. Hong, Rho, Yee, P.Y., 2007 (ii) nucleons lifted to a single isospin ½ 5D spinor 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

  17. leading in leading in

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

  19. Kim, Lee, P.Y. 2009 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)

  20. Kim, Lee, P.Y. 2009 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), nucleon

  21. Hong, Rho, Yee, P.Y., 2007 predictions for nucleon-meson interactions from 5D minimal term nucleon from 5D tensor term Hoehler, Pietarinen, 1975 Stoks, Klomp, Terheggen, de Swart, 1994 Machleidt, 2001 Gross, Stadler, 2007 nucleon

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

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

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

  25. NN repulsive core of solitonic baryon • 4D baryon # •  5D Coulomb charge • 5D Coulomb repulsion Kim, Zahed, 2009 Hashimoto, Sakai, Sugimoto, 2009 Lee, Kim, P.Y., 2009

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

  27. 2. String Theory Origin

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

  29. Maldacena 1997 from IIA holographic QCD without flavor D4

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  44. size of a single baryon, again, in ADHM Matrix QM ? minimizing the approximate energy functional Hashimoto, Iizuka, P.Y. 2010

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

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

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

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

  49. baryon size comparison

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