Abstract
A new method to study nuclear physics via holographic QCD is proposed. Multiple baryons in the Sakai-Sugimoto background are described by a matrix model which is a low energy effective theory of D-branes of the baryon vertices. We study the quantum mechanics of the matrix model and calculate the eigenstates of the Hamiltonian. The obtained states are found to coincide with known nuclear and baryonic states, and have appropriate statistics and charges. Calculated spectra of the baryon/nucleus for small baryon numbers show good agreement with experimental data. For hyperons, the Gell-Mann–Okubo formula is approximately derived. Baryon resonances up to spin 5/2 and isospin 5/2 and dibaryon spectra are obtained and compared with experimental data. The model partially explains even the magic numbers of light nuclei, N = 2, 8 and 20.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
K. Hashimoto, N. Iizuka and P. Yi, A Matrix Model for Baryons and Nuclear Forces, JHEP10 (2010) 003 [arXiv:1003.4988] [INSPIRE].
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys.38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett.B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys.2 (1998) 253 [hep-th/9802150] [INSPIRE].
G. ’t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys.B 72 (1974) 461 [INSPIRE].
E. Witten, Baryons in the 1/n Expansion, Nucl. Phys.B 160 (1979) 57 [INSPIRE].
T.H.R. Skyrme, A Unified Field Theory Of Mesons And Baryons, Nucl. Phys.31 (1962) 556.
T.H.R. Skyrme, A nonlinear field theory, Proc. Roy. Soc. Lond.A 260 (1961) 127 [INSPIRE].
T.H.R. Skyrme, Particle states of a quantized meson field, Proc. Roy. Soc. Lond.A 262 (1961) 237 [INSPIRE].
T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys.113 (2005) 843 [hep-th/0412141] [INSPIRE].
T. Sakai and S. Sugimoto, More on a holographic dual of QCD, Prog. Theor. Phys.114 (2005) 1083 [hep-th/0507073] [INSPIRE].
D.K. Hong, M. Rho, H.-U. Yee and P. Yi, Chiral Dynamics of Baryons from String Theory, Phys. Rev.D 76 (2007) 061901 [hep-th/0701276] [INSPIRE].
H. Hata, T. Sakai, S. Sugimoto and S. Yamato, Baryons from instantons in holographic QCD, Prog. Theor. Phys.117 (2007) 1157 [hep-th/0701280] [INSPIRE].
H. Hata, M. Murata and S. Yamato, Chiral currents and static properties of nucleons in holographic QCD, Phys. Rev.D 78 (2008) 086006 [arXiv:0803.0180] [INSPIRE].
D.K. Hong, M. Rho, H.-U. Yee and P. Yi, Dynamics of baryons from string theory and vector dominance, JHEP09 (2007) 063 [arXiv:0705.2632] [INSPIRE].
D.K. Hong, M. Rho, H.-U. Yee and P. Yi, Nucleon form-factors and hidden symmetry in holographic QCD, Phys. Rev.D 77 (2008) 014030 [arXiv:0710.4615] [INSPIRE].
K. Hashimoto, T. Sakai and S. Sugimoto, Holographic Baryons: Static Properties and Form Factors from Gauge/String Duality, Prog. Theor. Phys.120 (2008) 1093 [arXiv:0806.3122] [INSPIRE].
K.-Y. Kim and I. Zahed, Electromagnetic Baryon Form Factors from Holographic QCD, JHEP09 (2008) 007 [arXiv:0807.0033] [INSPIRE].
K. Hashimoto, T. Sakai and S. Sugimoto, Nuclear Force from String Theory, Prog. Theor. Phys.122 (2009) 427 [arXiv:0901.4449] [INSPIRE].
Y. Kim, S. Lee and P. Yi, Holographic Deuteron and Nucleon-Nucleon Potential, JHEP04 (2009) 086 [arXiv:0902.4048] [INSPIRE].
K.-Y. Kim and I. Zahed, Nucleon-Nucleon Potential from Holography, JHEP03 (2009) 131 [arXiv:0901.0012] [INSPIRE].
V. Kaplunovsky and J. Sonnenschein, Searching for an Attractive Force in Holographic Nuclear Physics, JHEP05 (2011) 058 [arXiv:1003.2621] [INSPIRE].
A. Cherman and T. Ishii, Long-distance properties of baryons in the Sakai-Sugimoto model, Phys. Rev.D 86 (2012) 045011 [arXiv:1109.4665] [INSPIRE].
J. Park and P. Yi, A Holographic QCD and Excited Baryons from String Theory, JHEP06 (2008) 011 [arXiv:0804.2926] [INSPIRE].
H.R. Grigoryan, T.S.H. Lee and H.-U. Yee, Electromagnetic Nucleon-to-Delta Transition in Holographic QCD, Phys. Rev.D 80 (2009) 055006 [arXiv:0904.3710] [INSPIRE].
A. Pomarol and A. Wulzer, Baryon Physics in Holographic QCD, Nucl. Phys.B 809 (2009) 347 [arXiv:0807.0316] [INSPIRE].
M.R. Pahlavani, J. Sadeghi and R. Morad, Binding energy of a holographic deuteron and tritium in anti-de-Sitter space/conformal field theory (AdS/CFT), Phys. Rev.C 82 (2010) 025201 [arXiv:1309.0640] [INSPIRE].
M.R. Pahlavani and R. Morad, Application of AdS/CFT in Nuclear Physics, Adv. High Energy Phys.2014 (2014) 863268 [arXiv:1403.2501] [INSPIRE].
S. Baldino, S. Bolognesi, S.B. Gudnason and D. Koksal, Solitonic approach to holographic nuclear physics, Phys. Rev.D 96 (2017) 034008 [arXiv:1703.08695] [INSPIRE].
S. Bolognesi and P. Sutcliffe, A low-dimensional analogue of holographic baryons, J. Phys.A 47 (2014) 135401 [arXiv:1311.2685] [INSPIRE].
K.-Y. Kim, S.-J. Sin and I. Zahed, The Chiral Model of Sakai-Sugimoto at Finite Baryon Density, JHEP01 (2008) 002 [arXiv:0708.1469] [INSPIRE].
M. Rozali, H.-H. Shieh, M. Van Raamsdonk and J. Wu, Cold Nuclear Matter In Holographic QCD, JHEP01 (2008) 053 [arXiv:0708.1322] [INSPIRE].
K.-Y. Kim, S.-J. Sin and I. Zahed, Dense holographic QCD in the Wigner-Seitz approximation, JHEP09 (2008) 001 [arXiv:0712.1582] [INSPIRE].
M. Rho, S.-J. Sin and I. Zahed, Dense QCD: A Holographic Dyonic Salt, Phys. Lett.B 689 (2010) 23 [arXiv:0910.3774] [INSPIRE].
V. Kaplunovsky, D. Melnikov and J. Sonnenschein, Baryonic Popcorn, JHEP11 (2012) 047 [arXiv:1201.1331] [INSPIRE].
V. Kaplunovsky, D. Melnikov and J. Sonnenschein, Holographic Baryons and Instanton Crystals, Mod. Phys. Lett.B 29 (2015) 1540052 [arXiv:1501.04655] [INSPIRE].
K. Hashimoto and N. Iizuka, Three-Body Nuclear Forces from a Matrix Model, JHEP11 (2010) 058 [arXiv:1005.4412] [INSPIRE].
K. Hashimoto and N. Iizuka, Nucleon Statistics in Holographic QCD: Aharonov-Bohm Effect in a Matrix Model, Phys. Rev.D 82 (2010) 105023 [arXiv:1006.3612] [INSPIRE].
S. Aoki, K. Hashimoto and N. Iizuka, Matrix Theory for Baryons: An Overview of Holographic QCD for Nuclear Physics, Rept. Prog. Phys.76 (2013) 104301 [arXiv:1203.5386] [INSPIRE].
K. Hashimoto, N. Iizuka and T. Nakatsukasa, N-Body Nuclear Forces at Short Distances in Holographic QCD, Phys. Rev.D 81 (2010) 106003 [arXiv:0911.1035] [INSPIRE].
K. Hashimoto and T. Morita, Nucleus from String Theory, Phys. Rev.D 84 (2011) 046004 [arXiv:1103.5688] [INSPIRE].
K. Hashimoto, Holographic Nuclei, Prog. Theor. Phys.121 (2009) 241 [arXiv:0809.3141] [INSPIRE].
K. Hashimoto, Holographic Nuclei: Supersymmetric Examples, JHEP12 (2009) 065 [arXiv:0910.2303] [INSPIRE].
M.F. Atiyah, N.J. Hitchin, V.G. Drinfeld and Yu.I. Manin, Construction of Instantons, Phys. Lett.A 65 (1978) 185 [INSPIRE].
E. Witten, Small instantons in string theory, Nucl. Phys.B 460 (1996) 541 [hep-th/9511030] [INSPIRE].
M.R. Douglas, Branes within branes, NATO Sci. Ser. C520 (1999) 267 [hep-th/9512077] [INSPIRE].
E. Witten, Baryons and branes in anti-de Sitter space, JHEP07 (1998) 006 [hep-th/9805112] [INSPIRE].
D.J. Gross and H. Ooguri, Aspects of large N gauge theory dynamics as seen by string theory, Phys. Rev.D 58 (1998) 106002 [hep-th/9805129] [INSPIRE].
D. Tong and C. Turner, Quantum Hall effect in supersymmetric Chern-Simons theories, Phys. Rev.B 92 (2015) 235125 [arXiv:1508.00580] [INSPIRE].
N. Dorey, D. Tong and C. Turner, Matrix model for non-Abelian quantum Hall states, Phys. Rev.B 94 (2016) 085114 [arXiv:1603.09688] [INSPIRE].
A. Barns-Graham, N. Dorey, N. Lohitsiri, D. Tong and C. Turner, ADHM and the 4d Quantum Hall Effect, JHEP04 (2018) 040 [arXiv:1710.09833] [INSPIRE].
M. Lüscher, Some Analytic Results Concerning the Mass Spectrum of Yang-Mills Gauge Theories on a Torus, Nucl. Phys.B 219 (1983) 233 [INSPIRE].
G. Mandal, M. Mahato and T. Morita, Phases of one dimensional large N gauge theory in a 1/D expansion, JHEP02 (2010) 034 [arXiv:0910.4526] [INSPIRE].
T. Hotta, J. Nishimura and A. Tsuchiya, Dynamical aspects of large N reduced models, Nucl. Phys.B 545 (1999) 543 [hep-th/9811220] [INSPIRE].
T. Morita, Thermodynamics of Large N Gauge Theories with Chemical Potentials in a 1/D Expansion, JHEP08 (2010) 015 [arXiv:1005.2181] [INSPIRE].
G. Mandal and T. Morita, Phases of a two dimensional large N gauge theory on a torus, Phys. Rev.D 84 (2011) 085007 [arXiv:1103.1558] [INSPIRE].
O. Aharony, J. Marsano, S. Minwalla and T. Wiseman, Black hole-black string phase transitions in thermal 1+1 dimensional supersymmetric Yang-Mills theory on a circle, Class. Quant. Grav.21 (2004) 5169 [hep-th/0406210] [INSPIRE].
O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas, M. Van Raamsdonk and T. Wiseman, The phase structure of low dimensional large N gauge theories on Tori, JHEP01 (2006) 140 [hep-th/0508077] [INSPIRE].
N. Kawahara, J. Nishimura and S. Takeuchi, Phase structure of matrix quantum mechanics at finite temperature, JHEP10 (2007) 097 [arXiv:0706.3517] [INSPIRE].
T. Azuma, T. Morita and S. Takeuchi, Hagedorn Instability in Dimensionally Reduced Large-N Gauge Theories as Gregory-Laflamme and Rayleigh-Plateau Instabilities, Phys. Rev. Lett.113 (2014) 091603 [arXiv:1403.7764] [INSPIRE].
D.N. Kabat and G. Lifschytz, Approximations for strongly coupled supersymmetric quantum mechanics, Nucl. Phys.B 571 (2000) 419 [hep-th/9910001] [INSPIRE].
D.N. Kabat, G. Lifschytz and D.A. Lowe, Black hole thermodynamics from calculations in strongly coupled gauge theory, Int. J. Mod. Phys.A 16 (2001) 856 [hep-th/0007051] [INSPIRE].
D.N. Kabat, G. Lifschytz and D.A. Lowe, Black hole entropy from nonperturbative gauge theory, Phys. Rev.D 64 (2001) 124015 [hep-th/0105171] [INSPIRE].
N. Iizuka, D.N. Kabat, G. Lifschytz and D.A. Lowe, Probing black holes in nonperturbative gauge theory, Phys. Rev.D 65 (2002) 024012 [hep-th/0108006] [INSPIRE].
J. Nishimura and F. Sugino, Dynamical generation of four-dimensional space-time in the IIB matrix model, JHEP05 (2002) 001 [hep-th/0111102] [INSPIRE].
H. Kawai, S. Kawamoto, T. Kuroki, T. Matsuo and S. Shinohara, Mean field approximation of IIB matrix model and emergence of four-dimensional space-time, Nucl. Phys.B 647 (2002) 153 [hep-th/0204240] [INSPIRE].
J. Nishimura, T. Okubo and F. Sugino, Convergent Gaussian expansion method: Demonstration in reduced Yang-Mills integrals, JHEP10 (2002) 043 [hep-th/0205253] [INSPIRE].
O. Aharony and D. Kutasov, Holographic Duals of Long Open Strings, Phys. Rev.D 78 (2008) 026005 [arXiv:0803.3547] [INSPIRE].
K. Hashimoto, T. Hirayama, F.-L. Lin and H.-U. Yee, Quark Mass Deformation of Holographic Massless QCD, JHEP07 (2008) 089 [arXiv:0803.4192] [INSPIRE].
R. Casero, E. Kiritsis and A. Paredes, Chiral symmetry breaking as open string tachyon condensation, Nucl. Phys.B 787 (2007) 98 [hep-th/0702155] [INSPIRE].
O. Bergman, S. Seki and J. Sonnenschein, Quark mass and condensate in HQCD, JHEP12 (2007) 037 [arXiv:0708.2839] [INSPIRE].
A. Dhar and P. Nag, Sakai-Sugimoto model, Tachyon Condensation and Chiral symmetry Breaking, JHEP01 (2008) 055 [arXiv:0708.3233] [INSPIRE].
K. Hashimoto, T. Hirayama and D.K. Hong, Quark Mass Dependence of Hadron Spectrum in Holographic QCD, Phys. Rev.D 81 (2010) 045016 [arXiv:0906.0402] [INSPIRE].
K. Hashimoto, N. Iizuka, T. Ishii and D. Kadoh, Three-flavor quark mass dependence of baryon spectra in holographic QCD, Phys. Lett.B 691 (2010) 65 [arXiv:0910.1179] [INSPIRE].
F. Bigazzi and P. Niro, Neutron-proton mass difference from gauge/gravity duality, Phys. Rev.D 98 (2018) 046004 [arXiv:1803.05202] [INSPIRE].
O.C. Druks, P.H.C. Lau and I. Zahed, Electromagnetic and Axial Current Form Factors and Spectroscopy of Three-Flavor Holographic Baryons, Phys. Rev.D 99 (2019) 054022 [arXiv:1807.05956] [INSPIRE].
M. Gell-Mann, The Eightfold Way: A Theory of strong interaction symmetry, CTSL-20, TID-12608.
S. Okubo, Note on unitary symmetry in strong interactions, Prog. Theor. Phys.27 (1962) 949 [INSPIRE].
S. Okubo, Note on Unitary Symmetry in Strong Interaction. II Excited States of Baryons, Prog. Theor. Phys.28 (1962) 24 [INSPIRE].
H. Clement, On the History of Dibaryons and their Final Observation, Prog. Part. Nucl. Phys.93 (2017) 195 [arXiv:1610.05591] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, Phys. Rev.D 98 (2018) 030001 [INSPIRE].
T. Banks, W. Fischler, S.H. Shenker and L. Susskind, M theory as a matrix model: A Conjecture, Phys. Rev.D 55 (1997) 5112 [hep-th/9610043] [INSPIRE].
P.M. Stevenson, Optimized Perturbation Theory, Phys. Rev.D 23 (1981) 2916 [INSPIRE].
M. Bashkanov et al., Double-Pionic Fusion of Nuclear Systems and the ABC Effect: Aproaching a Puzzle by Exclusive and Kinematically Complete Measurements, Phys. Rev. Lett.102 (2009) 052301 [arXiv:0806.4942] [INSPIRE].
WASA-at-COSY collaboration, ABC Effect in Basic Double-Pionic Fusion — Observation of a new resonance?, Phys. Rev. Lett.106 (2011) 242302 [arXiv:1104.0123] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1902.07444
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Hashimoto, K., Matsuo, Y. & Morita, T. Nuclear states and spectra in holographic QCD. J. High Energ. Phys. 2019, 1 (2019). https://doi.org/10.1007/JHEP12(2019)001
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2019)001