Towards a classification of branes in theories with eight supercharges

Open Access
Article

Abstract

We provide a classification of half-supersymmetric branes in quarter-maximal supergravity theories with scalars parametrising coset manifolds. We show that the results previously obtained for the half-maximal theories give evidence that half-supersymmetric branes correspond to the real longest weights of the representations of the brane charges, where the reality properties of the weights are determined from the Tits-Satake diagrams associated to the global symmetry groups. We show that the resulting brane structure is universal for all theories that can be uplifted to six dimensions. We also show that when viewing these theories as low-energy theories for the suitably compactified heterotic string, the classification we obtain is in perfect agreement with the wrapping rules derived in previous works for the same theory compactified on tori. Finally, we relate the branes to the R-symmetry representations of the central charges and we show that in general the degeneracies of the BPS conditions are twice those of the half-maximal theories and four times those of the maximal ones.

Keywords

p-branes String Duality 

References

  1. [1]
    S. Ferrara and J.M. Maldacena, Branes, central charges and U duality invariant BPS conditions, Class. Quant. Grav. 15 (1998) 749 [hep-th/9706097] [INSPIRE].ADSCrossRefMATHMathSciNetGoogle Scholar
  2. [2]
    S. Ferrara and M. Günaydin, Orbits of exceptional groups, duality and BPS states in string theory, Int. J. Mod. Phys. A 13 (1998) 2075 [hep-th/9708025] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    H. Lü, C.N. Pope and K.S. Stelle, Multiplet structures of BPS solitons, Class. Quant. Grav. 15 (1998) 537 [hep-th/9708109] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  4. [4]
    B.R. Greene, A.D. Shapere, C. Vafa and S.-T. Yau, Stringy cosmic strings and noncompact Calabi-Yau manifolds, Nucl. Phys. B 337 (1990) 1 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  5. [5]
    G.W. Gibbons, M.B. Green and M.J. Perry, Instantons and seven-branes in type IIB superstring theory, Phys. Lett. B 370 (1996) 37 [hep-th/9511080] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  6. [6]
    L.J. Romans, Massive N = 2a supergravity in ten-dimensions, Phys. Lett. B 169 (1986) 374 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  7. [7]
    J. Polchinski and E. Witten, Evidence for heterotic-type-I string duality, Nucl. Phys. B 460 (1996) 525 [hep-th/9510169] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  8. [8]
    J. Polchinski, Dirichlet branes and Ramond-Ramond charges, Phys. Rev. Lett. 75 (1995) 4724 [hep-th/9510017] [INSPIRE].ADSCrossRefMATHMathSciNetGoogle Scholar
  9. [9]
    C. Angelantonj and A. Sagnotti, Open strings, Phys. Rept. 371 (2002) 1 [Erratum ibid. 376 (2003) 339] [hep-th/0204089] [INSPIRE].
  10. [10]
    E.A. Bergshoeff, M. de Roo, S.F. Kerstan and F. Riccioni, IIB supergravity revisited, JHEP 08 (2005) 098 [hep-th/0506013] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    E.A. Bergshoeff, M. de Roo, S.F. Kerstan, T. Ortín and F. Riccioni, IIA ten-forms and the gauge algebras of maximal supergravity theories, JHEP 07 (2006) 018 [hep-th/0602280] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    E.A. Bergshoeff, J. Hartong, P.S. Howe, T. Ortín and F. Riccioni, IIA/IIB supergravity and ten-forms, JHEP 05 (2010) 061 [arXiv:1004.1348] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    F. Riccioni and P.C. West, The E 11 origin of all maximal supergravities, JHEP 07 (2007) 063 [arXiv:0705.0752] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  14. [14]
    E.A. Bergshoeff, I. De Baetselier and T.A. Nutma, E 11 and the embedding tensor, JHEP 09 (2007) 047 [arXiv:0705.1304] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    P.C. West, E 11 and M-theory, Class. Quant. Grav. 18 (2001) 4443 [hep-th/0104081] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  16. [16]
    B. de Wit, H. Nicolai and H. Samtleben, Gauged supergravities, tensor hierarchies and M-theory, JHEP 02 (2008) 044 [arXiv:0801.1294] [INSPIRE].CrossRefGoogle Scholar
  17. [17]
    H. Nicolai and H. Samtleben, Maximal gauged supergravity in three-dimensions, Phys. Rev. Lett. 86 (2001) 1686 [hep-th/0010076] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  18. [18]
    B. de Wit, H. Samtleben and M. Trigiante, On Lagrangians and gaugings of maximal supergravities, Nucl. Phys. B 655 (2003) 93 [hep-th/0212239] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    E.A. Bergshoeff and F. Riccioni, The D-brane U-scan, arXiv:1109.1725 [INSPIRE].
  20. [20]
    E.A. Bergshoeff, A. Marrani and F. Riccioni, Brane orbits, Nucl. Phys. B 861 (2012) 104 [arXiv:1201.5819] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  21. [21]
    A. Kleinschmidt, Counting supersymmetric branes, JHEP 10 (2011) 144 [arXiv:1109.2025] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  22. [22]
    E.A. Bergshoeff, F. Riccioni and L. Romano, Branes, weights and central charges, JHEP 06 (2013) 019 [arXiv:1303.0221] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  23. [23]
    E.A. Bergshoeff and F. Riccioni, String solitons and T-duality, JHEP 05 (2011) 131 [arXiv:1102.0934] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  24. [24]
    E.A. Bergshoeff and F. Riccioni, Branes and wrapping rules, Phys. Lett. B 704 (2011) 367 [arXiv:1108.5067] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  25. [25]
    E.A. Bergshoeff and F. Riccioni, Heterotic wrapping rules, JHEP 01 (2013) 005 [arXiv:1210.1422] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  26. [26]
    L. Borsten, M.J. Duff, S. Ferrara, A. Marrani and W. Rubens, Small orbits, Phys. Rev. D 85 (2012) 086002 [arXiv:1108.0424] [INSPIRE].ADSGoogle Scholar
  27. [27]
    E.A. Bergshoeff and F. Riccioni, Dual doubled geometry, Phys. Lett. B 702 (2011) 281 [arXiv:1106.0212] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  28. [28]
    E.A. Bergshoeff, C. Condeescu, G. Pradisi and F. Riccioni, Heterotic-type II duality and wrapping rules, JHEP 12 (2013) 057 [arXiv:1311.3578] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    E.A. Bergshoeff, T. Ortín and F. Riccioni, Defect branes, Nucl. Phys. B 856 (2012) 210 [arXiv:1109.4484] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    S. Araki, On root systems and an infinitesimal classification of irreducible symmetric spaces, J. Math 13 (1962) 1, Osaka City University, Osaka Japan (1962).
  31. [31]
    S. Helgason, Differential geometry, Lie groups and symmetric spaces, Pure and applied mathematics 80, Academic Press, New York U.S.A. (1978).Google Scholar
  32. [32]
    M. Henneaux, D. Persson and P. Spindel, Spacelike singularities and hidden symmetries of gravity, Living Rev. Rel. 11 (2008) 1 [arXiv:0710.1818] [INSPIRE].Google Scholar
  33. [33]
    L.J. Romans, Selfduality for interacting fields: covariant field equations for six-dimensional chiral supergravities, Nucl. Phys. B 276 (1986) 71 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  34. [34]
    M. Günaydin, G. Sierra and P.K. Townsend, Exceptional supergravity theories and the MAGIC square, Phys. Lett. B 133 (1983) 72 [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    M. Günaydin, G. Sierra and P.K. Townsend, The geometry of N = 2 Maxwell-Einstein supergravity and Jordan algebras, Nucl. Phys. B 242 (1984) 244 [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    M. Günaydin, G. Sierra and P.K. Townsend, More on d = 5 Maxwell-Einstein supergravity: symmetric spaces and kinks, Class. Quant. Grav. 3 (1986) 763 [INSPIRE].ADSCrossRefMATHGoogle Scholar
  37. [37]
    A. Kleinschmidt and D. Roest, Extended symmetries in supergravity: the semi-simple case, JHEP 07 (2008) 035 [arXiv:0805.2573] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  38. [38]
    F. Riccioni, A. Van Proeyen and P.C. West, Real forms of very extended Kac-Moody algebras and theories with eight supersymmetries, JHEP 05 (2008) 079 [arXiv:0801.2763] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    A. Keurentjes, The group theory of oxidation, Nucl. Phys. B 658 (2003) 303 [hep-th/0210178] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  40. [40]
    A. Keurentjes, The group theory of oxidation 2: cosets of nonsplit groups, Nucl. Phys. B 658 (2003) 348 [hep-th/0212024] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  41. [41]
    I. Schnakenburg and P.C. West, Kac-Moody symmetries of ten-dimensional nonmaximal supergravity theories, JHEP 05 (2004) 019 [hep-th/0401196] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  42. [42]
    E.A. Bergshoeff, J. Gomis, T.A. Nutma and D. Roest, Kac-Moody spectrum of (half-)maximal supergravities, JHEP 02 (2008) 069 [arXiv:0711.2035] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  43. [43]
    E.A. Bergshoeff and F. Riccioni, D-brane Wess-Zumino terms and U-duality, JHEP 11 (2010) 139 [arXiv:1009.4657] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  44. [44]
    M. Bianchi and A. Sagnotti, On the systematics of open string theories, Phys. Lett. B 247 (1990) 517 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  45. [45]
    M. Bianchi and A. Sagnotti, Twist symmetry and open string Wilson lines, Nucl. Phys. B 361 (1991) 519 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  46. [46]
    E.A. Bergshoeff, A. Kleinschmidt and F. Riccioni, Supersymmetric domain walls, Phys. Rev. D 86 (2012) 085043 [arXiv:1206.5697] [INSPIRE].ADSGoogle Scholar
  47. [47]
    E. Bergshoeff, F. Coomans, R. Kallosh, C.S. Shahbazi and A. Van Proeyen, Dirac-Born-Infeld-Volkov-Akulov and deformation of supersymmetry, JHEP 08 (2013) 100 [arXiv:1303.5662] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    C.M. Hull, A geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  49. [49]
    C.M. Hull, Doubled geometry and T-folds, JHEP 07 (2007) 080 [hep-th/0605149] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  50. [50]
    C.M. Hull and R.A. Reid-Edwards, Gauge symmetry, T-duality and doubled geometry, JHEP 08 (2008) 043 [arXiv:0711.4818] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  51. [51]
    G. Aldazabal, D. Marques and C. Núñez, Double field theory: a pedagogical review, Class. Quant. Grav. 30 (2013) 163001 [arXiv:1305.1907] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    J. de Boer and M. Shigemori, Exotic branes and non-geometric backgrounds, Phys. Rev. Lett. 104 (2010) 251603 [arXiv:1004.2521] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  53. [53]
    J. de Boer and M. Shigemori, Exotic branes in string theory, Phys. Rept. 532 (2013) 65 [arXiv:1209.6056] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Eric A. Bergshoeff
    • 1
  • Fabio Riccioni
    • 2
  • Luca Romano
    • 3
  1. 1.Centre for Theoretical PhysicsUniversity of GroningenGroningenThe Netherlands
  2. 2.INFN Sezione di Roma, Dipartimento di FisicaUniversità di Roma “La Sapienza”RomaItaly
  3. 3.Dipartimento di Fisica and INFN Sezione di RomaUniversità di Roma “La Sapienza”RomaItaly

Personalised recommendations