Journal of High Energy Physics

, 2013:42 | Cite as

p-brane actions and higher Roytenberg brackets

Article

Abstract

Motivated by the quest to understand the analog of non-geometric flux compactification in the context of M-theory, we study higher dimensional analogs of generalized Poisson sigma models and corresponding dual string and p-brane models. We find that higher generalizations of the algebraic structures due to Dorfman, Roytenberg and Courant play an important role and establish their relation to Nambu-Poisson structures.

Keywords

Flux compactifications p-branes Sigma Models 

References

  1. [1]
    J. Shelton, W. Taylor and B. Wecht, Nongeometric flux compactifications, JHEP 10 (2005) 085 [hep-th/0508133] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    A. Dabholkar and C. Hull, Generalised T-duality and non-geometric backgrounds, JHEP 05 (2006) 009 [hep-th/0512005] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    R. Blumenhagen, A. Deser, D. Lüst, E. Plauschinn and F. Rennecke, Non-geometric fluxes, asymmetric strings and nonassociative geometry, J. Phys. A 44 (2011) 385401 [arXiv:1106.0316] [INSPIRE].ADSGoogle Scholar
  4. [4]
    D. Mylonas, P. Schupp and R.J. Szabo, Membrane σ-models and quantization of non-geometric flux backgrounds, JHEP 09 (2012) 012 [arXiv:1207.0926] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    N. Ikeda, Two-dimensional gravity and nonlinear gauge theory, Annals Phys. 235 (1994) 435 [hep-th/9312059] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  6. [6]
    P. Schaller and T. Strobl, Poisson structure induced (topological) field theories, Mod. Phys. Lett. A 9 (1994) 3129 [hep-th/9405110] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    M. Kontsevich, Deformation quantization of Poisson manifolds. ., Lett. Math. Phys. 66 (2003) 157 [q-alg/9709040] [INSPIRE].
  8. [8]
    N. Ikeda, Lectures on AKSZ topological field theories for physicists, arXiv:1204.3714 [INSPIRE].
  9. [9]
    M.J. Duff and J.X. Lu, Duality rotations in membrane theory, Nucl. Phys. B 347 (1990) 394 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  10. [10]
    M. Bojowald, A. Kotov and T. Strobl, Lie algebroid morphisms, Poisson σ-models and off-shell closed gauge symmetries, J. Geom. Phys. 54 (2005) 400 [math/0406445] [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  11. [11]
    A. Kotov and T. Strobl, Generalizing geometryAlgebroids and σ-models, in Handbook of pseudo-Riemannian geometry and supersymmetry, V. Cortes ed., European Mathematical Society, Zürich, Switzerland (2012), arXiv:1004.0632 [INSPIRE].
  12. [12]
    A. Kotov, P. Schaller and T. Strobl, Dirac σ-models, Commun. Math. Phys. 260 (2005) 455 [hep-th/0411112] [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  13. [13]
    A. Alekseev and T. Strobl, Current algebras and differential geometry, JHEP 03 (2005) 035 [hep-th/0410183] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    N. Hitchin, Generalized Calabi-Yau manifolds, Quart. J. Math. Oxford Ser. 54 (2003) 281 [math/0209099] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    M. Gualtieri, Generalized complex geometry, math/0401221 [INSPIRE].
  16. [16]
    J. Ekstrand and M. Zabzine, Courant-like brackets and loop spaces, JHEP 03 (2011) 074 [arXiv:0903.3215] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    G. Bonelli and M. Zabzine, From current algebras for p-branes to topological M-theory, JHEP 09 (2005) 015 [hep-th/0507051] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  18. [18]
    T. Asakawa, S. Sasa and S. Watamura, D-branes in generalized geometry and Dirac-Born-Infeld action, JHEP 10 (2012) 064 [arXiv:1206.6964] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  19. [19]
    N. Halmagyi, Non-geometric string backgrounds and worldsheet algebras, JHEP 07 (2008) 137 [arXiv:0805.4571] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  20. [20]
    N. Halmagyi, Non-geometric backgrounds and the first order string σ-model, arXiv:0906.2891 [INSPIRE].
  21. [21]
    L. Takhtajan, On foundation of the generalized Nambu mechanics, Commun. Math. Phys. 160 (1994) 295 [hep-th/9301111] [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  22. [22]
    J. Bagger and N. Lambert, Modeling multiple M2’s, Phys. Rev. D 75 (2007) 045020 [hep-th/0611108] [INSPIRE].MathSciNetADSGoogle Scholar
  23. [23]
    J. Bagger, N. Lambert, S. Mukhi and C. Papageorgakis, Multiple membranes in M-theory, arXiv:1203.3546 [INSPIRE].
  24. [24]
    D.S. Berman and M.J. Perry, Generalized geometry and M theory, JHEP 06 (2011) 074 [arXiv:1008.1763] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  25. [25]
    D.S. Berman, H. Godazgar, M. Godazgar and M.J. Perry, The local symmetries of M-theory and their formulation in generalised geometry, JHEP 01 (2012) 012 [arXiv:1110.3930] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  26. [26]
    D.S. Berman, M. Cederwall, A. Kleinschmidt and D.C. Thompson, The gauge structure of generalised diffeomorphisms, JHEP 01 (2013) 064 [arXiv:1208.5884] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    B. Jurčo and P. Schupp, Nambu-σ-model and effective membrane actions, Phys. Lett. B 713 (2012) 313 [arXiv:1203.2910] [INSPIRE].ADSGoogle Scholar
  28. [28]
    P. Bouwknegt and B. Jurčo, AKSZ construction of topological open p-brane action and Nambu brackets, arXiv:1110.0134 [INSPIRE].
  29. [29]
    P. Schupp and B. Jurčo, Nambu σ-model and branes, PoS(CORFU2011)045 [arXiv:1205.2595] [INSPIRE].
  30. [30]
    S. Deser and B. Zumino, A complete action for the spinning string, Phys. Lett. B 65 (1976) 369 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  31. [31]
    L. Brink, P. Di Vecchia and P.S. Howe, A locally supersymmetric and reparametrization invariant action for the spinning string, Phys. Lett. B 65 (1976) 471 [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    P.S. Howe and R. Tucker, A locally supersymmetric and reparametrization invariant action for a spinning membrane, J. Phys. A 10 (1977) L155 [INSPIRE].ADSGoogle Scholar
  33. [33]
    L. Baulieu, A.S. Losev, and N.A. Nekrasov, Target space symmetries in topological theories. 1, JHEP 02 (2002) 021 [hep-th/0106042] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  34. [34]
    D. Roytenberg, A note on quasi Lie bialgebroids and twisted Poisson manifolds, Lett. Math. Phys. 61 (2002) 123 [math/0112152] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  35. [35]
    Y. Bi and Y. Sheng, On higher analogues of Courant algebroids, Sci. China A 54 (2011) 437.MathSciNetCrossRefGoogle Scholar
  36. [36]
    M. Zambon, L-infinity algebras and higher analogues of Dirac structures and Courant algebroids, J. Symplectic Geom. 10N4 (2012) 1 [arXiv:1003.1004] [INSPIRE].MathSciNetGoogle Scholar
  37. [37]
    S. Guttenberg, Brackets, σ-models and Integrability of Generalized Complex Structures, JHEP 06 (2007) 004 [hep-th/0609015] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  38. [38]
    Y. Hagiwara, Nambu-Dirac manifolds, J. Phys. A 35 (2002) 1263.MathSciNetADSGoogle Scholar
  39. [39]
    D. Alekseevsky and P. Guha, On decomposability of Nambu-Poisson tensor, Acta Math. Univ. Comenianae LXV (1996) 1.MathSciNetGoogle Scholar
  40. [40]
    J. Wess and B. Zumino, Consequences of anomalous Ward identities, Phys. Lett. B 37 (1971) 95 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  41. [41]
    E. Witten, Nonabelian bosonization in two-dimensions, Commun. Math. Phys. 92 (1984) 455.MathSciNetADSCrossRefMATHGoogle Scholar
  42. [42]
    M. Zabzine, Lectures on generalized complex geometry and supersymmetry, Archivum Math. 42 (2006) 119 [hep-th/0605148] [INSPIRE].MathSciNetMATHGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Mathematical Institute, Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic
  2. 2.Jacobs University BremenBremenGermany
  3. 3.Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical EngineeringPragueCzech Republic

Personalised recommendations