Noncommutative geometry of multicore bions



We find new BPS solutions to the nonabelian theory on a world-volume of parallel D1-branes. Our solutions describe two parallel, separated bundles of N D1-branes expanding out to form a single orthogonal D3-brane. This configuration corresponds to two charge N magnetic monopoles in the world-volume of a single D3-brane, deforming the D3-brane into two parallel spikes. We obtain the emergent surface corresponding to our nonabelian D1-brane configuration and demonstrate, at finite N , a surprisingly accurate agreement with the shape of the D3-brane world-volume as obtained from the abelian Born-Infeld action. Our solution provides an explicit realization of topology change in noncommutative geometry at finite N.


Solitons Monopoles and Instantons D-branes Non-Commutative Geometry 


  1. [1]
    A.A. Tseytlin, On nonabelian generalization of Born-Infeld action in string theory, Nucl. Phys. B 501 (1997) 41 [hep-th/9701125] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    R.C. Myers, Dielectric branes, JHEP 12 (1999) 022 [hep-th/9910053] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    M.R. Douglas, Branes within branes, hep-th/9512077 [INSPIRE].
  4. [4]
    C.G. Callan and J.M. Maldacena, Brane death and dynamics from the Born-Infeld action, Nucl. Phys. B 513 (1998) 198 [hep-th/9708147] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    G. Gibbons, Born-Infeld particles and Dirichlet p-branes, Nucl. Phys. B 514 (1998) 603 [hep-th/9709027] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    N.R. Constable, R.C. Myers and O. Tafjord, The noncommutative bion core, Phys. Rev. D 61 (2000) 106009 [hep-th/9911136] [INSPIRE].MathSciNetADSGoogle Scholar
  7. [7]
    D. Berenstein and E. Dzienkowski, Matrix embeddings on flat R 3 and the geometry of membranes, Phys. Rev. D 86 (2012) 086001 [arXiv:1204.2788] [INSPIRE].ADSGoogle Scholar
  8. [8]
    X. Chen and E.J. Weinberg, ADHMN boundary conditions from removing monopoles, Phys. Rev. D 67 (2003) 065020 [hep-th/0212328] [INSPIRE].MathSciNetADSGoogle Scholar
  9. [9]
    P.M. Sutcliffe, BPS monopoles, Int. J. Mod. Phys. A 12 (1997) 4663 [hep-th/9707009] [INSPIRE].MathSciNetADSGoogle Scholar
  10. [10]
    P.L. Cook, R. de Mello Koch and J. Murugan, Nonabelian bionic brane intersections, Phys. Rev. D 68 (2003) 126007 [hep-th/0306250] [INSPIRE].ADSGoogle Scholar
  11. [11]
    N.R. Constable and N.D. Lambert, Calibrations, monopoles and fuzzy funnels, Phys. Rev. D 66 (2002)065016 [hep-th/0206243] [INSPIRE].MathSciNetADSGoogle Scholar
  12. [12]
    N.R. Constable, R.C. Myers and O. Tafjord, Fuzzy funnels: nonabelian brane intersections, hep-th/0105035 [INSPIRE].
  13. [13]
    N.R. Constable, R.C. Myers and O. Tafjord, Nonabelian brane intersections, JHEP 06 (2001)023 [hep-th/0102080] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    R. Bhattacharyya and R. de Mello Koch, Fluctuating fuzzy funnels, JHEP 10 (2005) 036 [hep-th/0508131] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    G. Grignani, T. Harmark, A. Marini, N.A. Obers and M. Orselli, Heating up the BIon, JHEP 06 (2011) 058 [arXiv:1012.1494] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    G. Grignani, T. Harmark, A. Marini, N.A. Obers and M. Orselli, Thermodynamics of the hot BIon, Nucl. Phys. B 851 (2011) 462 [arXiv:1101.1297] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    D.-E. Diaconescu, D-branes, monopoles and Nahm equations, Nucl. Phys. B 503 (1997) 220 [hep-th/9608163] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  18. [18]
    D. Tsimpis, Nahm equations and boundary conditions, Phys. Lett. B 433 (1998) 287 [hep-th/9804081] [INSPIRE].MathSciNetADSGoogle Scholar
  19. [19]
    A. Kapustin and S. Sethi, The Higgs branch of impurity theories, Adv. Theor. Math. Phys. 2 (1998)571 [hep-th/9804027] [INSPIRE].MathSciNetMATHGoogle Scholar
  20. [20]
    C. Bachas, J. Hoppe and B. Pioline, Nahm equations, N = 1∗ domain walls and D strings in AdS 5 × S 5, JHEP 07 (2001) 041 [hep-th/0007067] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  21. [21]
    C. Funnel, D1-brane description of separated magnetic monopoles on a D3-brane, undergraduate thesis, University of British Columbia, Vancouver Canada (2007).Google Scholar

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© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Department of Physics and AstronomyUniversity of British ColumbiaVancouverCanada

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