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Journal of High Energy Physics

, 2010:16 | Cite as

New potentials from Scherk-Schwarz reductions

  • Hugo Looyestijn
  • Erik PlauschinnEmail author
  • Stefan Vandoren
Article

Abstract

We study compactifications of eleven-dimensional supergravity on Calabi-Yau threefolds times a circle, with a duality twist along the circle a la Scherk-Schwarz. This leads to four-dimensional \( \mathcal{N} = 2 \) gauged supergravity with a semi-positive definite potential for the scalar fields, which we derive explicitly. Furthermore, inspired by the orientifold projection in string theory, we define a truncation to \( \mathcal{N} = 1 \) supergravity. We determine the D-terms, Kähler-and superpotentials for these models and study the properties of the vacua. Finally, we point out a relation to M-theory compactifications on seven-dimensional manifolds with G 2 structure.

Keywords

Supergravity Models M-Theory 

References

  1. [1]
    J. Scherk and J.H. Schwarz, Spontaneous breaking of supersymmetry through dimensional reduction, Phys. Lett. B 82 (1979) 60 [SPIRES].ADSGoogle Scholar
  2. [2]
    J. Scherk and J.H. Schwarz, How to get masses from extra dimensions, Nucl. Phys. B 153 (1979) 61 [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  3. [3]
    E. Bergshoeff, M. de Roo and E. Eyras, Gauged supergravity from dimensional reduction, Phys. Lett. B 413 (1997) 70 [hep-th/9707130] [SPIRES].ADSGoogle Scholar
  4. [4]
    I.V. Lavrinenko, H. Lü and C.N. Pope, Fibre bundles and generalised dimensional reductions, Class. Quant. Grav. 15 (1998) 2239 [hep-th/9710243] [SPIRES].CrossRefzbMATHADSGoogle Scholar
  5. [5]
    C.M. Hull, Gauged D = 9 supergravities and Scherk-Schwarz reduction, Class. Quant. Grav. 21 (2004) 509 [hep-th/0203146] [SPIRES].CrossRefzbMATHADSMathSciNetGoogle Scholar
  6. [6]
    L. Andrianopoli, R. D’Auria, S. Ferrara and M.A. Lledó, Gauging of flat groups in four dimensional supergravity, JHEP 07 (2002) 010 [hep-th/0203206] [SPIRES].CrossRefADSGoogle Scholar
  7. [7]
    A. Dabholkar and C. Hull, Duality twists, orbifolds and fluxes, JHEP 09 (2003) 054 [hep-th/0210209] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  8. [8]
    B. de Wit, H. Samtleben and M. Trigiante, On Lagrangians and gaugings of maximal supergravities, Nucl. Phys. B 655 (2003) 93 [hep-th/0212239] [SPIRES].ADSGoogle Scholar
  9. [9]
    L. Andrianopoli, S. Ferrara and M.A. Lledó, Scherk-Schwarz reduction of D = 5 special and quaternionic geometry, Class. Quant. Grav. 21 (2004) 4677 [hep-th/0405164] [SPIRES].CrossRefzbMATHADSGoogle Scholar
  10. [10]
    G. Dall’Agata and S. Ferrara, Gauged supergravity algebras from twisted tori compactifications with fluxes, Nucl. Phys. B 717 (2005) 223 [hep-th/0502066] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  11. [11]
    L. Andrianopoli, M.A. Lledó and M. Trigiante, The Scherk-Schwarz mechanism as a flux compactification with internal torsion, JHEP 05 (2005) 051 [hep-th/0502083] [SPIRES].CrossRefADSGoogle Scholar
  12. [12]
    C.M. Hull and R.A. Reid-Edwards, Flux compactifications of string theory on twisted tori, Fortsch. Phys. 57 (2009) 862 [hep-th/0503114] [SPIRES].CrossRefzbMATHMathSciNetGoogle Scholar
  13. [13]
    G. Dall’Agata and N. Prezas, Scherk-Schwarz reduction of M-theory on G2-manifolds with fluxes, JHEP 10 (2005) 103 [hep-th/0509052] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  14. [14]
    C.M. Hull and R.A. Reid-Edwards, Flux compactifications of M-theory on twisted tori, JHEP 10 (2006) 086 [hep-th/0603094] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  15. [15]
    O. Aharony, M. Berkooz, J. Louis and A. Micu, Non-Abelian structures in compactifications of M-theory on seven-manifolds with SU(3) structure, JHEP 09 (2008) 108 [arXiv:0806.1051] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  16. [16]
    T.W. Grimm and J. Louis, The effective action of type IIA Calabi-Yau orientifolds, Nucl. Phys. B 718 (2005) 153 [hep-th/0412277] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  17. [17]
    C. Beasley and E. Witten, A note on fluxes and superpotentials in M-theory compactifications on manifolds of G 2 holonomy, JHEP 07 (2002) 046 [hep-th/0203061] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  18. [18]
    T. House and A. Micu, M-theory compactifications on manifolds with G 2 structure, Class. Quant. Grav. 22 (2005) 1709 [hep-th/0412006] [SPIRES].CrossRefzbMATHADSMathSciNetGoogle Scholar
  19. [19]
    S. Gukov, Solitons, superpotentials and calibrations, Nucl. Phys. B 574 (2000) 169 [hep-th/9911011] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  20. [20]
    B.S. Acharya and B.J. Spence, Flux, supersymmetry and M-theory on 7-manifolds, hep-th/0007213 [SPIRES].
  21. [21]
    E. Cremmer, B. Julia, and J. Scherk, Supergravity theory in 11 dimensions, Phys. Lett. B 76 (1978) 409 [SPIRES].ADSGoogle Scholar
  22. [22]
    A.C. Cadavid, A. Ceresole, R. D’Auria and S. Ferrara, Eleven-dimensional supergravity compactified on Calabi-Yau threefolds, Phys. Lett. B 357 (1995) 76 [hep-th/9506144] [SPIRES].ADSMathSciNetGoogle Scholar
  23. [23]
    M. Gunaydin, G. Sierra, and P.K. Townsend, Gauging the d = 5 Maxwell-Einstein supergravity theories: more on Jordan algebras, Nucl. Phys. B 253 (1985) 573 [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  24. [24]
    E. Bergshoeff et al., N = 2 supergravity in five dimensions revisited, Class. Quant. Grav. 21 (2004) 3015 [Class. Quant. Grav. 23 (2006) 7149] [hep-th/0403045] [SPIRES].CrossRefzbMATHADSMathSciNetGoogle Scholar
  25. [25]
    B. de Wit and A. Van Proeyen, Broken σ-model isometries in very special geometry, Phys. Lett. B 293 (1992) 94 [hep-th/9207091] [SPIRES].ADSGoogle Scholar
  26. [26]
    B. de Wit and A. Van Proeyen, Special geometry, cubic polynomials and homogeneous quaternionic spaces, Commun. Math. Phys. 149 (1992) 307 [hep-th/9112027] [SPIRES].CrossRefzbMATHADSGoogle Scholar
  27. [27]
    B. de Wit, F. Vanderseypen and A. Van Proeyen, Symmetry structure of special geometries, Nucl. Phys. B 400 (1993) 463 [hep-th/9210068] [SPIRES].CrossRefADSGoogle Scholar
  28. [28]
    B. de Wit, P.G. Lauwers, and A. Van Proeyen, Lagrangians of N = 2 supergravity-matter systems, Nucl. Phys. B 255 (1985) 569 [SPIRES].ADSGoogle Scholar
  29. [29]
    K. Hristov, H. Looyestijn and S. Vandoren, Maximally supersymmetric solutions of D = 4 N = 2 gauged supergravity, JHEP 11 (2009) 115 [arXiv:0909.1743] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  30. [30]
    L. Andrianopoli et al., N = 2 supergravity and N = 2 super Yang-Mills theory on general scalar manifolds: Symplectic covariance, gaugings and the momentum map, J. Geom. Phys. 23 (1997) 111 [hep-th/9605032] [SPIRES].CrossRefzbMATHADSMathSciNetGoogle Scholar
  31. [31]
    B. de Wit, M. Roček and S. Vandoren, Gauging isometries on hyperKähler cones and quaternion-Kähler manifolds, Phys. Lett. B 511 (2001) 302 [hep-th/0104215] [SPIRES].ADSGoogle Scholar
  32. [32]
    S. Kachru and J. McGreevy, M-theory on manifolds of G 2 holonomy and type IIA orientifolds, JHEP 06 (2001) 027 [hep-th/0103223] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  33. [33]
    D. Joyce, Compact Riemannian 7-manifolds with holonomy G2. I, J. Diff. Geom. 43 (1996) 291.zbMATHMathSciNetGoogle Scholar
  34. [34]
    D. Joyce, Compact Riemannian 7-manifolds with holonomy G2. II, J. Diff. Geom. 43 (1996) 329zbMATHMathSciNetGoogle Scholar
  35. [35]
    N.J. Hitchin, The geometry of three-forms in six and seven dimensions, math/0010054 [SPIRES].
  36. [36]
    S. Chiossi and S. Salamon, The intrinsic torsion of SU(3) and G 2 structures, math/0202282 [SPIRES].
  37. [37]
    A. Micu, E. Palti and P.M. Saffin, M-theory on seven-dimensional manifolds with SU(3) structure, JHEP 05 (2006) 048 [hep-th/0602163] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  38. [38]
    J.A. Harvey and G.W. Moore, Superpotentials and membrane instantons, hep-th/9907026 [SPIRES].
  39. [39]
    J. Gutowski and G. Papadopoulos, Moduli spaces and brane solitons for M-theory compactifications on holonomy G 2 anifolds, Nucl. Phys. B 615 (2001) 237 [hep-th/0104105] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  40. [40]
    A. Strominger, Yukawa couplings in superstring compactification, Phys. Rev. Lett. 55 (1985) 2547 [SPIRES].CrossRefADSGoogle Scholar
  41. [41]
    G. Tian, Smoothness of the universal deformation space of compact Calabi-Yau manifolds and its Weil-Peterson metric, in Mathematical Aspects of String Theory, S.-T. Yau ed., pg. 629, World Scientific, Singapore Singapore (1987).Google Scholar
  42. [42]
    A. Strominger, Special geometry, Commun. Math. Phys. 133 (1990) 163 [SPIRES].CrossRefzbMATHADSMathSciNetGoogle Scholar
  43. [43]
    P. Candelas and X. de la Ossa, Moduli space of Calabi-Yau manifolds, Nucl. Phys. B 355 (1991) 455 [SPIRES].CrossRefADSGoogle Scholar
  44. [44]
    H. Suzuki, Calabi-Yau compactification of type IIB string and a mass formula of the extreme black holes, Mod. Phys. Lett. A 11 (1996) 623 [hep-th/9508001] [SPIRES].ADSGoogle Scholar
  45. [45]
    A. Ceresole, R. D’Auria and S. Ferrara, The symplectic structure of N = 2 supergravity and its central extension, Nucl. Phys. Proc. Suppl. 46 (1996) 67 [hep-th/9509160] [SPIRES].CrossRefzbMATHADSMathSciNetGoogle Scholar
  46. [46]
    J. Louis and A. Micu, Type II theories compactified on Calabi-Yau threefolds in the presence of background fluxes, Nucl. Phys. B 635 (2002) 395 [hep-th/0202168] [SPIRES].CrossRefADSMathSciNetGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  • Hugo Looyestijn
    • 1
  • Erik Plauschinn
    • 1
    • 2
    Email author
  • Stefan Vandoren
    • 1
  1. 1.Institute for Theoretical Physics and Spinoza InstituteUtrecht UniversityUtrechtThe Netherlands
  2. 2.Kavli Institute for Theoretical Physics, Kohn HallUCSBSanta BarbaraU.S.A.

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