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Journal of High Energy Physics

, 2014:137 | Cite as

Emergent bubbling geometries in gauge theories with SU(2|4) symmetry

  • Yuhma AsanoEmail author
  • Goro Ishiki
  • Shinji Shimasaki
Open Access
Article
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Abstract

We study the gauge/gravity duality between bubbling geometries in type IIA supergravity and gauge theories with SU(2|4) symmetry, which consist of \( \mathcal{N}=4 \) super Yang-Mills on R × S 3/Z k , \( \mathcal{N}=8 \) super Yang-Mills on R × S 2 and the plane wave matrix model. We show that the geometries are realized as field configurations in the strong coupling region of the gauge theories. On the gravity side, the bubbling geometries can be mapped to electrostatic systems with conducting disks. We derive integral equations which determine the charge densities on the disks. On the gauge theory side, we obtain a matrix integral by applying the localization to a 1/4-BPS sector of the gauge theories. The eigenvalue densities of the matrix integral turn out to satisfy the same integral equations as the charge densities on the gravity side. Thus we find that these two objects are equivalent.

Keywords

Gauge-gravity correspondence M(atrix) Theories Supersymmetric gauge theory Field Theories in Lower Dimensions 
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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.

References

  1. [1]
    J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
  2. [2]
    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].MathSciNetCrossRefADSGoogle Scholar
  3. [3]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].MathSciNetzbMATHADSGoogle Scholar
  4. [4]
    I.R. Klebanov, String theory in two-dimensions, in Trieste 1991, Proceedings, String theory and quantum gravity ’91, 30-101 and Princeton University (1991), PUPT-1271 [hep-th/9108019] [INSPIRE].
  5. [5]
    P.H. Ginsparg and G.W. Moore, Lectures on 2D gravity and 2D string theory (TASI 1992), in Boulder 1992, Proceedings, Recent directions in particle theory, 277-469 and Yale University, New Haven (1992), YCTP-P23-92, LA-UR-92-3479 [hep-th/9304011] [INSPIRE].
  6. [6]
    S. Mukhi, Topological matrix models, Liouville matrix model and c = 1 string theory, hep-th/0310287 [INSPIRE].
  7. [7]
    H. Lin, O. Lunin and J.M. Maldacena, Bubbling AdS space and 1/2 BPS geometries, JHEP 10 (2004) 025 [hep-th/0409174] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  8. [8]
    S. Yamaguchi, Bubbling geometries for half BPS Wilson lines, Int. J. Mod. Phys. A 22 (2007) 1353 [hep-th/0601089] [INSPIRE].CrossRefADSGoogle Scholar
  9. [9]
    D.E. Berenstein, A Toy model for the AdS/CFT correspondence, JHEP 07 (2004) 018 [hep-th/0403110] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  10. [10]
    Y. Takayama and A. Tsuchiya, Complex matrix model and fermion phase space for bubbling AdS geometries, JHEP 10 (2005) 004 [hep-th/0507070] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  11. [11]
    H. Mori and S. Yamaguchi, M5-branes and Wilson Surfaces in AdS 7 /CFT 6 Correspondence, Phys. Rev. D 90 (2014) 026005 [arXiv:1404.0930] [INSPIRE].ADSGoogle Scholar
  12. [12]
    Y. Asano, G. Ishiki, T. Okada and S. Shimasaki, Emergent bubbling geometries in the plane wave matrix model, JHEP 05 (2014) 075 [arXiv:1401.5079] [INSPIRE].CrossRefADSGoogle Scholar
  13. [13]
    H. Lin and J.M. Maldacena, Fivebranes from gauge theory, Phys. Rev. D 74 (2006) 084014 [hep-th/0509235] [INSPIRE].MathSciNetADSGoogle Scholar
  14. [14]
    D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N = 4 super Yang-Mills, JHEP 04 (2002) 013 [hep-th/0202021] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  15. [15]
    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].MathSciNetADSGoogle Scholar
  16. [16]
    H. Ling, A.R. Mohazab, H.-H. Shieh, G. van Anders and M. Van Raamsdonk, Little string theory from a double-scaled matrix model, JHEP 10 (2006) 018 [hep-th/0606014] [INSPIRE].CrossRefADSGoogle Scholar
  17. [17]
    V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  18. [18]
    Y. Asano, G. Ishiki, T. Okada and S. Shimasaki, Exact results for perturbative partition functions of theories with SU(2|4) symmetry, JHEP 02 (2013) 148 [arXiv:1211.0364] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  19. [19]
    J.M. Maldacena, M.M. Sheikh-Jabbari and M. Van Raamsdonk, Transverse five-branes in matrix theory, JHEP 01 (2003) 038 [hep-th/0211139] [INSPIRE].CrossRefADSGoogle Scholar
  20. [20]
    M. Berkooz, M. Rozali and N. Seiberg, Matrix description of M-theory on T 4 and T 5, Phys. Lett. B 408 (1997) 105 [hep-th/9704089] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  21. [21]
    N. Seiberg, New theories in six-dimensions and matrix description of M-theory on T 5 and \( {T}^5/{\mathrm{\mathbb{Z}}}_2 \), Phys. Lett. B 408 (1997) 98 [hep-th/9705221] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  22. [22]
    O. Aharony, A Brief review of ‘little string theories’, Class. Quant. Grav. 17 (2000) 929 [hep-th/9911147] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  23. [23]
    D. Kutasov, Introduction to little string theory, in Superstrings and related matters. Proceedings, Spring School, Trieste, Italy, April 2–10, 2001, C. Bachas, J. Martin Maldacena, K.S. Narain and S. Randjbar-Daemi eds., ICTP, Trieste (2001) [INSPIRE].
  24. [24]
    G. Ishiki, S. Shimasaki, Y. Takayama and A. Tsuchiya, Embedding of theories with SU(2|4) symmetry into the plane wave matrix model, JHEP 11 (2006) 089 [hep-th/0610038] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  25. [25]
    W. Taylor, D-brane field theory on compact spaces, Phys. Lett. B 394 (1997) 283 [hep-th/9611042] [INSPIRE].CrossRefADSGoogle Scholar
  26. [26]
    T. Ishii, G. Ishiki, S. Shimasaki and A. Tsuchiya, T-duality, fiber bundles and matrices, JHEP 05 (2007) 014 [hep-th/0703021] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  27. [27]
    H. Ling, H.-H. Shieh and G. van Anders, Little String Theory from Double-Scaling Limits of Field Theories, JHEP 02 (2007) 031 [hep-th/0611019] [INSPIRE].CrossRefADSGoogle Scholar
  28. [28]
    I.N. Sneddon, Mixed boundary value problems in potential theory, North-Holland, Amsterdam (1966).zbMATHGoogle Scholar
  29. [29]
    B. Chen et al., Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity, JHEP 10 (2007) 003 [arXiv:0704.2233] [INSPIRE].CrossRefADSGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Department of PhysicsKyoto UniversityKitashirakawaJapan
  2. 2.Yukawa Institute for Theoretical PhysicsKyoto UniversityKitashirakawaJapan
  3. 3.Theory CenterHigh Energy Accelerator Research Organization (KEK)OhoJapan

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