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Precision Holographic Baryons PILJIN YI (KIAS) Baryons 2010, Osaka, December 2010 Koji Hashimoto Deog-Ki Hong Norihiro Iizuka Youngman Kim Sangmin Lee Jaemo Park Mannque Rho Ho-Ung Yee H. Hata K.Hashimoto T. Sakai S. Sugimoto S. Yamato ?

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with a string theoretical holographic QCD model of very few adjustable parameters, can one do qualitative/quantitative particle physics of baryons and mesons ?

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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: 4D flavor symmetry 5D flavor gauge symmetry

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Sakai, Sugimoto., 2004

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chiral symmetry = 5D large gauge transformation

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D8’s anti-D8’s D8’s D4’s string theory origin: nonAdS/nonCFT with D4/D8-branes

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vs an extra UV parameter that appears because the underlying color theory is an open string theory and becomes QCD only at low energy IR flavor coupling function: it dictates all couplings and mass distributions (with ) in the flavor sector warp factor

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1.holography keeps color-singlets ( large N_c master fields) only: no trace of original color indices remains in the dual string theory in 5D 3.holographic description becomes a controllable effective field theory, as stringy components become decoupled 2.holography elevates a continuous global symmetry to a gauge symmetry: 4D flavor symmetry 5D flavor gauge theory

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Sakai, Sugimoto., 2004

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starting with this holographic effective action of mesons, realize the baryon as a coherent state (quantized soliton) & derive the effective action thereof with no new parameter

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Hong, Rho, Yee, P.Y., 2007 to be used at tree-level only, as dictated by the holography

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5D 4D : pseudoscalars & spin 1 mesons massive spin 1 mesons from gauge-Higgsing pseudoscalars from open Wilson line

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5D flavor gauge theory 4D chiral theory of mesons

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extrapolation to real QCD

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Sakai+Sugimoto, 2004

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also, consistent with E. Witten’s large N_c prediction ! NPB156, (1979)

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2.holography elevates a continuous global symmetry to a gauge symmetry: 4D flavor symmetry 5D flavor gauge theory baryon number 5D gauge U(1) charge

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U(1) charge = N solitonic baryon

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classical size Hong, Rho, Yee, Yi, hep-th/ Hata, Sakai, Sugimoto, Yamato, hep-th/ this soliton size has little to do with either the charge radius or with the repulsive core seen by NN the latter two are separately computable and dictated by the couplings to spin 1 mesons and their masses

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Compton size << soliton size << meson Compton sizes the shape of the classical soliton is trustworthy, yet, it can still be treated point-like for interaction with mesons the baryon field

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then, after a long song and dance…….

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

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5D minimal coupling 5D mass function 5D tensor coupling Hong, Rho, Yee, P.Y., 2007 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

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

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

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an effective action for 4D nucleons/mesons

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nucleon iso-singlet/triplet (axial-)vector mesons quartic terms also present but not shown

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all tensor couplings vanish identically, (meaning that coefficients of the respective leading 1/ N behavior vanish, and, thus, is NOT a consequence of large N counting) except for those associated with the tower of rho mesons Kim, Lee, P.Y numbers

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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), Kim, Lee, P.Y. 2009

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from 5D minimal term from 5D tensor term numbers nucleon Hoehler, Pietarinen, 1975 Stoks, Klomp, Terheggen, de Swart, 1994 Machleidt, 2001 Gross, Stadler, 2007

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numbers nucleon pions nucleon it represents about 1/3 improvement over that of the Skyrmion picture a la Adkins-Nappi-Witten at 0.61

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numbers nucleon pions nucleon ? Hong, Rho, Yee, P.Y.,2007

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E&M charge form factor: complete vector dominance again

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NN potential

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a universal repulsive core between baryons from 5D Coulomb repulsion due to the baryon number as a gauge U(1) charge Kim, Zahed, 2009 Hashimoto, Sakai, Sugimoto, 2009 Lee, Kim, P.Y., 2009

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two-body nucleon potential from meson exchanges: large N limit Kim, Lee, P.Y. 2009

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two-body nucleon potential from meson exchanges: N=3

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issues quenched no practical answer here, yet chiral limit mass deformation by a technicolor ? chiral condensate invisible string theory tachyon ? because of this(?), order one mismatch of mass scales between the glueball sector / the meson sector / the baryon sector

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things to do compute physical processes directly within this model for meaningful comparisons with data better handling of many nucleon system dense matter in general incorporation of gravity neutron star understand why such naïve extrapolation from holographic limit sometimes work at all for some quantities

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a stringy alternative to address many nucleon system ? matrix baryons K.Hashimoto, N.Iizuka, P.Y., 2010 next talk by Koji

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