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Quantum states to brane geometries via fuzzy moduli spaces of giant gravitons

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Abstract

Eighth-BPS local operators in \( \mathcal{N} = {4} \) SYM are dual to quantum states arising from the quantization of a moduli space of giant gravitons in AdS 5 × S 5. Earlier results on the quantization of this moduli space give a Hilbert space of multiple harmonic oscillators in 3 dimensions. We use these results, along with techniques from fuzzy geometry, to develop a map between quantum states and brane geometries. In particular there is a map between the oscillator states and points in a discretization of the base space in the toric fibration of the moduli space. We obtain a geometrical decomposition of the space of BPS states with labels consisting of U(3) representations along with U(N) Young diagrams and associated group theoretic multiplicities. Factorization properties in the counting of BPS states lead to predictions for BPS world-volume excitations of specific brane geometries. Some of our results suggest an intriguing complementarity between localisation in the moduli space of branes and localisation in space-time.

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References

  1. 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) 1133] [hep-th/9711200] [INSPIRE].

  2. 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 

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

    MathSciNet  ADS  MATH  Google Scholar 

  4. J. McGreevy, L. Susskind and N. Toumbas, Invasion of the giant gravitons from Anti-de Sitter space, JHEP 06 (2000) 008 [hep-th/0003075] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. V. Balasubramanian, M. Berkooz, A. Naqvi and M.J. Strassler, Giant gravitons in conformal field theory, JHEP 04 (2002) 034 [hep-th/0107119] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. S. Corley, A. Jevicki and S. Ramgoolam, Exact correlators of giant gravitons from dual N = 4 SYM theory, Adv. Theor. Math. Phys. 5 (2002) 809[hep-th/0111222] [INSPIRE].

    MathSciNet  Google Scholar 

  7. A. Mikhailov, Giant gravitons from holomorphic surfaces, JHEP 11 (2000) 027 [hep-th/0010206] [INSPIRE].

    Article  ADS  Google Scholar 

  8. A. Hashimoto, S. Hirano and N. Itzhaki, Large branes in AdS and their field theory dual, JHEP 08 (2000) 051 [hep-th/0008016] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. M.T. Grisaru, R.C. Myers and O. Tafjord, SUSY and goliath, JHEP 08 (2000) 040 [hep-th/0008015] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. V. Balasubramanian, M.-x. Huang, T.S. Levi and A. Naqvi, Open strings from N = 4 super Yang-Mills, JHEP 08 (2002) 037 [hep-th/0204196] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. O. Aharony, Y.E. Antebi, M. Berkooz and R. Fishman, ’Holey sheets’: Pfaffians and subdeterminants as D-brane operators in large-N gauge theories, JHEP 12 (2002) 069 [hep-th/0211152] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  12. D. Berenstein, Shape and holography: Studies of dual operators to giant gravitons, Nucl. Phys. B 675 (2003) 179 [hep-th/0306090] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. V. Balasubramanian, D. Berenstein, B. Feng and M.-x. Huang, D-branes in Yang-Mills theory and emergent gauge symmetry, JHEP 03 (2005) 006 [hep-th/0411205] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  14. R. de Mello Koch, J. Smolic and M. Smolic, Giant Gravitons - with Strings Attached (I), JHEP 06 (2007) 074 [hep-th/0701066] [INSPIRE].

    Article  Google Scholar 

  15. R. de Mello Koch, J. Smolic and M. Smolic, Giant Gravitons - with Strings Attached (II), JHEP 09 (2007) 049 [hep-th/0701067] [INSPIRE].

    Article  Google Scholar 

  16. D. Bekker, R. de Mello Koch and M. Stephanou, Giant Gravitons - with Strings Attached. III., JHEP 02 (2008) 029 [arXiv:0710.5372] [INSPIRE].

    Article  ADS  Google Scholar 

  17. W. Carlson, R. de Mello Koch and H. Lin, Nonplanar Integrability, JHEP 03 (2011) 105 [arXiv:1101.5404] [INSPIRE].

    Article  ADS  Google Scholar 

  18. R. de Mello Koch, B.A.E. Mohammed and S. Smith, Nonplanar Integrability: Beyond the SU(2) Sector, arXiv:1106.2483 [INSPIRE].

  19. R. de Mello Koch, M. Dessein, D. Giataganas and C. Mathwin, Giant Graviton Oscillators, JHEP 10 (2011) 009 [arXiv:1108.2761] [INSPIRE].

    Article  Google Scholar 

  20. S.R. Das, A. Jevicki and S.D. Mathur, Vibration modes of giant gravitons, Phys. Rev. D 63 (2001) 024013 [hep-th/0009019] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  21. T.W. Brown, P. Heslop and S. Ramgoolam, Diagonal multi-matrix correlators and BPS operators in N = 4 SYM, JHEP 02 (2008) 030 [arXiv:0711.0176] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. T. Brown, Cut-and-join operators and N = 4 super Yang-Mills, JHEP 05 (2010) 058 [arXiv:1002.2099] [INSPIRE].

    Article  ADS  Google Scholar 

  23. Y. Kimura, Quarter BPS classified by Brauer algebra, JHEP 05 (2010) 103 [arXiv:1002.2424] [INSPIRE].

    Article  ADS  Google Scholar 

  24. J. Pasukonis and S. Ramgoolam, From counting to construction of BPS states in N = 4 SYM, JHEP 02 (2011) 078 [arXiv:1010.1683] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  25. Y. Kimura and H. Lin, Young diagrams, Brauer algebras and bubbling geometries, JHEP 01 (2012) 121 [arXiv:1109.2585] [INSPIRE].

    Article  ADS  Google Scholar 

  26. J. Kinney, J.M. Maldacena, S. Minwalla and S. Raju, An Index for 4 dimensional super conformal theories, Commun. Math. Phys. 275 (2007) 209 [hep-th/0510251] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. G. Mandal and N.V. Suryanarayana, Counting 1/8-BPS dual-giants, JHEP 03 (2007) 031 [hep-th/0606088] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. C.E. Beasley, BPS branes from baryons, JHEP 11 (2002) 015 [hep-th/0207125] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  29. I. Biswas, D. Gaiotto, S. Lahiri and S. Minwalla, Supersymmetric states of N = 4 Yang-Mills from giant gravitons, JHEP 12 (2007) 006 [hep-th/0606087] [INSPIRE]

    Article  MathSciNet  ADS  Google Scholar 

  30. A. Balachandran, B.P. Dolan, J.-H. Lee, X. Martin and D. O’Connor, Fuzzy complex projective spaces and their star products, J. Geom. Phys. 43 (2002) 184 [hep-th/0107099] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. G. Alexanian, A. Balachandran, G. Immirzi and B. Ydri, Fuzzy CP 2, J. Geom. Phys. 42 (2002) 28 [hep-th/0103023] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. H. Grosse and A. Strohmaier, Towards a nonperturbative covariant regularization in 4 − D quantum field theory, Lett. Math. Phys. 48 (1999) 163 [hep-th/9902138] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  33. C. Sämann, Fuzzy toric geometries, JHEP 02 (2008) 111 [hep-th/0612173] [INSPIRE].

    Article  ADS  Google Scholar 

  34. S.P. Trivedi and S. Vaidya, Fuzzy cosets and their gravity duals, JHEP 09 (2000) 041 [hep-th/0007011] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. V. Balasubramanian, J. de Boer, V. Jejjala and J. Simon, Entropy of near-extremal black holes in AdS 5, JHEP 05 (2008) 067 [arXiv:0707.3601] [INSPIRE].

    Article  ADS  Google Scholar 

  36. J.M. Maldacena and A. Strominger, AdS 3 black holes and a stringy exclusion principle, JHEP 12 (1998) 005 [hep-th/9804085] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. N. Woodhouse, Geometric Quantization, Clarendon Press, Oxford and New York (1980).

    MATH  Google Scholar 

  38. J.J. Heckman and H. Verlinde, Evidence for F(uzz) Theory, JHEP 01 (2011) 044 [arXiv:1005.3033] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  39. K. Furuuchi and K. Okuyama, D-branes Wrapped on Fuzzy del Pezzo Surfaces, JHEP 01 (2011) 043 [arXiv:1008.5012] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. A. Iqbal, A. Neitzke and C. Vafa, A Mysterious duality, Adv. Theor. Math. Phys. 5 (2002) 769 [hep-th/0111068] [INSPIRE].

    MathSciNet  Google Scholar 

  41. Simplex, http://en.wikipedia.org/wiki/Simplex.

  42. J. Madore, The Fuzzy sphere, Class. Quant. Grav. 9 (1992) 69 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  43. D. Martelli and J. Sparks, Dual Giant Gravitons in Sasaki-Einstein Backgrounds, Nucl. Phys. B 759 (2006) 292 [hep-th/0608060] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  44. A. Hamilton, J. Murugan and A. Prinsloo, Lessons from giant gravitons on AdS 5  × T 1,1, JHEP 06 (2010) 017 [arXiv:1001.2306] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  45. W. Fulton and J. Harris, Representation theory: a first course, Springer (1991).

  46. T.W. Brown, P. Heslop and S. Ramgoolam, Diagonal free field matrix correlators, global symmetries and giant gravitons, JHEP 04 (2009) 089 [arXiv:0806.1911] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  47. Y. Kimura and S. Ramgoolam, Enhanced symmetries of gauge theory and resolving the spectrum of local operators, Phys. Rev. D 78 (2008) 126003 [arXiv:0807.3696] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  48. T.W. Brown, Permutations and the Loop, JHEP 06 (2008) 008 [arXiv:0801.2094] [INSPIRE].

    Article  ADS  Google Scholar 

  49. D. Berenstein, D.H. Correa and S.E. Vazquez, A Study of open strings ending on giant gravitons, spin chains and integrability, JHEP 09 (2006) 065 [hep-th/0604123] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  50. A. Sen, Dyon - monopole bound states, selfdual harmonic forms on the multi - monopole moduli space and SL(2, \( \mathbb{Z} \)) invariance in string theory, Phys. Lett. B 329 (1994) 217 [hep-th/9402032] [INSPIRE].

    ADS  Google Scholar 

  51. E. Witten, Bound states of strings and p-branes, Nucl. Phys. B 460 (1996) 335 [hep-th/9510135] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  52. L. Maoz and V.S. Rychkov, Geometry quantization from supergravity: The Case of ’Bubbling AdS’, JHEP 08 (2005) 096 [hep-th/0508059] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  53. A. Jevicki and S. Ramgoolam, Noncommutative gravity from the AdS/CFT correspondence, JHEP 04 (1999) 032 [hep-th/9902059] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  54. S.D. Mathur, The Fuzzball proposal for black holes: An Elementary review, Fortsch. Phys. 53 (2005) 793 [hep-th/0502050] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  55. A. Bissi, C. Kristjansen, D. Young and K. Zoubos, Holographic three-point functions of giant gravitons, JHEP 06 (2011) 085 [arXiv:1103.4079] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  56. J. de Boer, M. Johnstone, M. Sheikh-Jabbari and J. Simon, Emergent IR Dual 2d CFTs in Charged AdS5 Black Holes, arXiv:1112.4664 [INSPIRE].

  57. H. Lin, O. Lunin and J.M. Maldacena, Bubbling AdS space and 1/2 BPS geometries, JHEP 10 (2004) 025 [hep-th/0409174] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  58. O. Lunin, Brane webs and 1/4-BPS geometries, JHEP 09 (2008) 028 [arXiv:0802.0735] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Queen Mary, University of London, Mile End Road, London, E1 4NS, U.K.

    Jurgis Pasukonis & Sanjaye Ramgoolam

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  1. Jurgis Pasukonis
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  2. Sanjaye Ramgoolam
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Correspondence to Jurgis Pasukonis.

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ArXiv ePrint: 1201.5588

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Pasukonis, J., Ramgoolam, S. Quantum states to brane geometries via fuzzy moduli spaces of giant gravitons. J. High Energ. Phys. 2012, 77 (2012). https://doi.org/10.1007/JHEP04(2012)077

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