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Baryonic popcorn

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Abstract

In the large N c limit cold dense nuclear matter must be in a lattice phase. This applies also to holographic models of hadron physics. In a class of such models, like the generalized Sakai-Sugimoto model, baryons take the form of instantons of the effective flavor gauge theory that resides on probe flavor branes. In this paper we study the phase structure of baryonic crystals by analyzing discrete periodic configurations of such instantons. We find that instanton configurations exhibit a series of “popcorn” transitions upon increasing the density. Through these transitions normal (3D) lattices expand into the transverse dimension, eventually becoming a higher dimensional (4D) multi-layer lattice at large densities.

We consider 3D lattices of zero size instantons as well as 1D periodic chains of finite size instantons, which serve as toy models of the full holographic systems. In particular, for the finite-size case we determine solutions of the corresponding ADHM equations for both a straight chain and for a 2D zigzag configuration where instantons pop up into the holographic dimension. At low density the system takes the form of an “abelian anti- ferromagnetic” straight periodic chain. Above a critical density there is a second order phase transition into a zigzag structure. An even higher density yields a rich phase space characterized by the formation of multi-layer zigzag structures. The finite size of the lattices in the transverse dimension is a signal of an emerging Fermi sea of quarks. We thus propose that the popcorn transitions indicate the onset of the “quarkyonic” phase of the cold dense nuclear matter.

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References

  1. K. Rajagopal and F. Wilczek, The Condensed matter physics of QCD, hep-ph/0011333 [INSPIRE].

  2. T. Schafer, Phases of QCD, hep-ph/0509068 [INSPIRE].

  3. M.G. Alford, Color superconductivity in ultra-dense quark matter, PoS(LAT2006)001 [hep-lat/0610046] [INSPIRE].

  4. M. Stephanov, QCD phase diagram: An Overview, PoS(LAT2006)024 [hep-lat/0701002] [INSPIRE].

  5. L. McLerran and R.D. Pisarski, Phases of cold, dense quarks at large-N c , Nucl. Phys. A 796 (2007) 83 [arXiv:0706.2191] [INSPIRE].

    ADS  Google Scholar 

  6. J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].

    MathSciNet  ADS  MATH  Google Scholar 

  7. 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].

    MathSciNet  ADS  Google Scholar 

  8. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].

    MathSciNet  ADS  MATH  Google Scholar 

  9. T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  10. E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  11. A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  12. M. Kruczenski, D. Mateos, R.C. Myers and D.J. Winters, Meson spectroscopy in AdS/CFT with flavor, JHEP 07 (2003) 049 [hep-th/0304032] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. M. Kruczenski, D. Mateos, R.C. Myers and D.J. Winters, Towards a holographic dual of large-N c QCD, JHEP 05 (2004) 041 [hep-th/0311270] [INSPIRE].

    Article  ADS  Google Scholar 

  14. J. Erdmenger, N. Evans, I. Kirsch and E. Threlfall, Mesons in Gauge/Gravity Duals - A Review, Eur. Phys. J. A 35 (2008) 81 [arXiv:0711.4467] [INSPIRE].

    ADS  Google Scholar 

  15. E. Witten, Baryons and branes in anti-de Sitter space, JHEP 07 (1998) 006 [hep-th/9805112] [INSPIRE].

    ADS  Google Scholar 

  16. 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].

    Article  ADS  MATH  Google Scholar 

  17. Y. Kim and D. Yi, Holography at work for nuclear and hadron physics, Adv. High Energy Phys. 2011 (2011) 259025 [arXiv:1107.0155] [INSPIRE].

    MathSciNet  Google Scholar 

  18. N. Horigome and Y. Tanii, Holographic chiral phase transition with chemical potential, JHEP 01 (2007) 072 [hep-th/0608198] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. S. Nakamura, Y. Seo, S.-J. Sin and K. Yogendran, A New Phase at Finite Quark Density from AdS/CFT, J. Korean Phys. Soc. 52 (2008) 1734 [hep-th/0611021] [INSPIRE].

    Article  ADS  Google Scholar 

  20. D. Yamada, Sakai-Sugimoto model at high density, JHEP 10 (2008) 020 [arXiv:0707.0101] [INSPIRE].

    Article  ADS  Google Scholar 

  21. O. Bergman, G. Lifschytz and M. Lippert, Holographic Nuclear Physics, JHEP 11 (2007) 056 [arXiv:0708.0326] [INSPIRE].

    Article  ADS  Google Scholar 

  22. M. Rozali, H.-H. Shieh, M. Van Raamsdonk and J. Wu, Cold Nuclear Matter In Holographic QCD, JHEP 01 (2008) 053 [arXiv:0708.1322] [INSPIRE].

    Article  ADS  Google Scholar 

  23. S. Kobayashi, D. Mateos, S. Matsuura, R.C. Myers and R.M. Thomson, Holographic phase transitions at finite baryon density, JHEP 02 (2007) 016 [hep-th/0611099] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. S.K. Domokos and J.A. Harvey, Baryon number-induced Chern-Simons couplings of vector and axial-vector mesons in holographic QCD, Phys. Rev. Lett. 99 (2007) 141602 [arXiv:0704.1604] [INSPIRE].

    Article  ADS  Google Scholar 

  25. Y. Kim, B.-H. Lee, S. Nam, C. Park and S.-J. Sin, Deconfinement phase transition in holographic QCD with matter, Phys. Rev. D 76 (2007) 086003 [arXiv:0706.2525] [INSPIRE].

    ADS  Google Scholar 

  26. Y. Kim, C.-H. Lee and H.-U. Yee, Holographic Nuclear Matter in AdS/QCD, Phys. Rev. D 77 (2008) 085030 [arXiv:0707.2637] [INSPIRE].

    ADS  Google Scholar 

  27. S.-J. Sin, Gravity back-reaction to the baryon density for bulk filling branes, JHEP 10 (2007) 078 [arXiv:0707.2719] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. A. Karch and A. O’Bannon, Holographic thermodynamics at finite baryon density: Some exact results, JHEP 11 (2007) 074 [arXiv:0709.0570] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  29. D. Mateos, S. Matsuura, R.C. Myers and R.M. Thomson, Holographic phase transitions at finite chemical potential, JHEP 11 (2007) 085 [arXiv:0709.1225] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. P. Basu, F. Nogueira, M. Rozali, J.B. Stang and M. Van Raamsdonk, Towards A Holographic Model of Color Superconductivity, New J. Phys. 13 (2011) 055001 [arXiv:1101.4042] [INSPIRE].

    Article  ADS  Google Scholar 

  31. M. Rho, S.-J. Sin and I. Zahed, Dense QCD: A Holographic Dyonic Salt, Phys. Lett. B 689 (2010) 23 [arXiv:0910.3774] [INSPIRE].

    ADS  Google Scholar 

  32. T. Skyrme, A Nonlinear field theory, Proc. Roy. Soc. Lond. A 260 (1961) 127 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  33. I.R. Klebanov, Nuclear Matter in the Syrme Model, Nucl. Phys. B 262 (1985) 133 [INSPIRE].

    Article  ADS  Google Scholar 

  34. A.S. Goldhaber and N. Manton, Maximal Symmetry of the Skyrme Crystal, Phys. Lett. B 198 (1987) 231 [INSPIRE].

    ADS  Google Scholar 

  35. M. Kugler and S. Shtrikman, A New Skyrmion Crystal, Phys. Lett. B 208 (1988) 491 [INSPIRE].

    ADS  Google Scholar 

  36. M. Kugler and S. Shtrikman, Skyrmion Crystals and their Symmetries, Phys. Rev. D 40 (1989) 3421 [INSPIRE].

    ADS  Google Scholar 

  37. A. Dymarsky, S. Kuperstein and J. Sonnenschein, Chiral Symmetry Breaking with non-SUSY D7-branes in ISD backgrounds, JHEP 08 (2009) 005 [arXiv:0904.0988] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: Duality cascades and chi SB resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  39. G. ’t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  40. E. Witten, Baryons in the 1/n Expansion, Nucl. Phys. B 160 (1979) 57 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  41. E. Witten, Current Algebra, Baryons and Quark Confinement, Nucl. Phys. B 223 (1983) 433 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  42. G.S. Adkins, C.R. Nappi and E. Witten, Static Properties of Nucleons in the Skyrme Model, Nucl. Phys. B 228 (1983) 552 [INSPIRE].

    Article  ADS  Google Scholar 

  43. A. Casher, Chiral Symmetry Breaking in Quark Confining Theories, Phys. Lett. B 83 (1979) 395 [INSPIRE].

    ADS  Google Scholar 

  44. T. Banks and A. Casher, Chiral Symmetry Breaking in Confining Theories, Nucl. Phys. B 169 (1980) 103 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  45. O. Aharony, J. Sonnenschein and S. Yankielowicz, A Holographic model of deconfinement and chiral symmetry restoration, Annals Phys. 322 (2007) 1420 [hep-th/0604161] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  46. D.B. Kaplan and A.V. Manohar, The Nucleon-nucleon potential in the 1/N c expansion, Phys. Rev. C 56 (1997) 76 [nucl-th/9612021] [INSPIRE].

    ADS  Google Scholar 

  47. V. Kaplunovsky and J. Sonnenschein, Searching for an Attractive Force in Holographic Nuclear Physics, JHEP 05 (2011) 058 [arXiv:1003.2621] [INSPIRE].

    Article  ADS  Google Scholar 

  48. L. Bonanno and F. Giacosa, Does nuclear matter bind at large-N c ?, Nucl. Phys. A 859 (2011) 49 [arXiv:1102.3367] [INSPIRE].

    ADS  Google Scholar 

  49. J. Verbaarschot and T. Wettig, Random matrix theory and chiral symmetry in QCD, Ann. Rev. Nucl. Part. Sci. 50 (2000) 343 [hep-ph/0003017] [INSPIRE].

    Article  ADS  Google Scholar 

  50. J. Osborn, K. Splittorff and J. Verbaarschot, Chiral symmetry breaking and the Dirac spectrum at nonzero chemical potential, Phys. Rev. Lett. 94 (2005) 202001 [INSPIRE].

    Article  ADS  Google Scholar 

  51. L.Y. Glozman and R. Wagenbrunn, Chirally symmetric but confining dense and cold matter, Phys. Rev. D 77 (2008) 054027 [arXiv:0709.3080] [INSPIRE].

    ADS  Google Scholar 

  52. D. Deryagin, D.Y. Grigoriev and V. Rubakov, Standing wave ground state in high density, zero temperature QCD at large-N c , Int. J. Mod. Phys. A 7 (1992) 659 [INSPIRE].

    ADS  Google Scholar 

  53. E. Shuster and D. Son, On finite density QCD at large-N c , Nucl. Phys. B 573 (2000) 434 [hep-ph/9905448] [INSPIRE].

    Article  ADS  Google Scholar 

  54. M. Kutschera, C. Pethick and D. Ravenhall, Dense matter in the chiral soliton model, Phys. Rev. Lett. 53 (1984) 1041 [INSPIRE].

    Article  ADS  Google Scholar 

  55. N. Manton and P. Ruback, Skyrmions in flat space and curved space, Phys. Lett. B 181 (1986) 137 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  56. M. Atiyah and N. Manton, Skyrmions from instantons, Phys. Lett. B 222 (1989) 438 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  57. B. Schroers, Dynamics of moving and spinning Skyrmions, Z. Phys. C 61 (1994) 479 [hep-ph/9308236] [INSPIRE].

    ADS  Google Scholar 

  58. C.J. Houghton, N.S. Manton and P.M. Sutcliffe, Rational maps, monopoles and Skyrmions, Nucl. Phys. B 510 (1998) 507 [hep-th/9705151] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  59. N. Manton, Is the B = 2 Skyrmion axially symmetric?, Phys. Lett. B 192 (1987) 177 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  60. E. Wuest, G. Brown and A. Jackson, Topological chiral bags in a baryonic environment, Nucl. Phys. A 468 (1987) 450 [INSPIRE].

    ADS  Google Scholar 

  61. A. Jackson, A. Wirzba and N. Manton, New Skyrmion solutions on a three sphere, Nucl. Phys. A 495 (1989) 499 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  62. H. Forkel, A. Jackson, M. Rho, C. Weiss, A. Wirzba and H. Bang, Chiral symmetry restoration and the Skyrme model, Nucl. Phys. A 504 (1989) 818 [INSPIRE].

    ADS  Google Scholar 

  63. P. Sutcliffe, Skyrmions, instantons and holography, JHEP 08 (2010) 019 [arXiv:1003.0023] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  64. K. Nawa, H. Suganuma and T. Kojo, Baryons in holographic QCD, Phys. Rev. D 75 (2007) 086003 [hep-th/0612187] [INSPIRE].

    ADS  Google Scholar 

  65. 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].

    MathSciNet  ADS  Google Scholar 

  66. A. Brandhuber, N. Itzhaki, J. Sonnenschein and S. Yankielowicz, Baryons from supergravity, JHEP 07 (1998) 020 [hep-th/9806158] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  67. C.G. Callan Jr., A. Guijosa, K.G. Savvidy and O. Tafjord, Baryons and flux tubes in confining gauge theories from brane actions, Nucl. Phys. B 555 (1999) 183 [hep-th/9902197] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  68. S. Seki and J. Sonnenschein, Comments on Baryons in Holographic QCD, JHEP 01 (2009) 053 [arXiv:0810.1633] [INSPIRE].

    Article  ADS  Google Scholar 

  69. E. Witten, σ-models and the ADHM construction of instantons, J. Geom. Phys. 15 (1995) 215 [hep-th/9410052] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  70. M.R. Douglas, Branes within branes, hep-th/9512077 [INSPIRE].

  71. M.R. Douglas, Gauge fields and D-branes, J. Geom. Phys. 28 (1998) 255 [hep-th/9604198] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  72. M. Atiyah, N.J. Hitchin, V. Drinfeld and Y. Manin, Construction of Instantons, Phys. Lett. A 65 (1978) 185 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  73. S. Kuperstein and J. Sonnenschein, Non-critical, near extremal AdS 6 background as a holographic laboratory of four dimensional YM theory, JHEP 11 (2004) 026 [hep-th/0411009] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  74. A. Dymarsky, D. Melnikov and J. Sonnenschein, Attractive Holographic Baryons, JHEP 06 (2011) 145 [arXiv:1012.1616] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  75. A. Pomarol and A. Wulzer, Baryon Physics in Holographic QCD, Nucl. Phys. B 809 (2009) 347 [arXiv:0807.0316] [INSPIRE].

    Article  ADS  Google Scholar 

  76. G. Panico and A. Wulzer, Nucleon Form Factors from 5D Skyrmions, Nucl. Phys. A 825 (2009) 91 [arXiv:0811.2211] [INSPIRE].

    ADS  Google Scholar 

  77. A. Cherman, T.D. Cohen and M. Nielsen, Model Independent Tests of Skyrmions and Their Holographic Cousins, Phys. Rev. Lett. 103 (2009) 022001 [arXiv:0903.2662] [INSPIRE].

    Article  ADS  Google Scholar 

  78. 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].

    ADS  Google Scholar 

  79. S. Kuperstein and J. Sonnenschein, A New Holographic Model of Chiral Symmetry Breaking, JHEP 09 (2008) 012 [arXiv:0807.2897] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  80. I.R. Klebanov and E. Witten, Superconformal field theory on three-branes at a Calabi-Yau singularity, Nucl. Phys. B 536 (1998) 199 [hep-th/9807080] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  81. K.-Y. Kim, S.-J. Sin and I. Zahed, Dense hadronic matter in holographic QCD, hep-th/0608046 [INSPIRE].

  82. K.-M. Lee and P. Yi, Monopoles and instantons on partially compactified D-branes, Phys. Rev. D 56 (1997) 3711 [hep-th/9702107] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  83. D. Harland and R. Ward, Chains of Skyrmions, JHEP 12 (2008) 093 [arXiv:0807.3870] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  84. T.C. Kraan and P. van Baal, Periodic instantons with nontrivial holonomy, Nucl. Phys. B 533 (1998) 627 [hep-th/9805168] [INSPIRE].

    Article  ADS  Google Scholar 

  85. B.J. Harrington and H.K. Shepard, Periodic Euclidean Solutions and the Finite Temperature Yang-Mills Gas, Phys. Rev. D 17 (1978) 2122 [INSPIRE].

    ADS  Google Scholar 

  86. P. Rossi, Propagation functions in the field of a monopole, Nucl. Phys. B 149 (1979) 170 [INSPIRE].

    Article  ADS  Google Scholar 

  87. H. Osborn, Calculation of multi - instanton determinants, Nucl. Phys. B 159 (1979) 497 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  88. W. Nahm, A Simple Formalism for the BPS Monopole, Phys. Lett. B 90 (1980) 413 [INSPIRE].

    ADS  Google Scholar 

  89. H.K. Lee and M. Rho, Half-Skyrmion Hadronic Matter at High Density, arXiv:0905.0235 [INSPIRE].

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Kaplunovsky, V., Melnikov, D. & Sonnenschein, J. Baryonic popcorn. J. High Energ. Phys. 2012, 47 (2012). https://doi.org/10.1007/JHEP11(2012)047

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