Skip to main content
SpringerLink
Log in

Non-Semisimple and Complex Gaugings of N=16 Supergravity

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

Maximal and non-maximal supergravities in three dimensions allow for a large variety of semisimple (Chern-Simons) gauge groups. In this paper, we analyze non-semisimple and complex gauge groups that satisfy the pertinent consistency relations for a maximal (N=16) gauged supergravity to exist. We give a general procedure how to generate non-semisimple gauge groups from known admissible semisimple gauge groups by a singular boost within E8(8). Examples include the theories with gauge group SO(8)×T28 that describe the reduction of IIA/IIB supergravity on the seven-sphere. In addition, we exhibit two ‘strange embeddings’ of the complex gauge group into (real) E8(8) and prove that both can be consistently gauged. We discuss the structure of the associated scalar potentials as well as their relation to those of D≥4 gauged supergravities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Andrianopoli, L., Cordaro, F., Fré, P., Gualtieri, L.: Non-semisimple gaugings of D=5 N=8 supergravity and FDAs. Class. Quantum Grav. 18, 395–413 (2001). hep-th/0009048

    Article  MathSciNet  MATH  Google Scholar 

  2. Andrianopoli, L., D’Auria, R., Ferrara, S., Lledó, M. A.: Gauging of flat groups in four dimensional supergravity. JHEP 07, 010 (2002). hep-th/0203206

    Article  Google Scholar 

  3. Cremmer, E., Julia, B.: The SO(8) supergravity. Nucl. Phys. B159, 141 (1979)

  4. Cremmer, E., Julia, B., Lu, H., Pope, C.N.: Dualisation of dualities. I. Nucl. Phys. B523, 73–144 (1998). hep-th/9710119

  5. Cvetič, M., Lu, H., Pope, C.N.: Consistent Kaluza-Klein sphere reductions. Phys. Rev. D62, 064028 (2000). hep-th/0003286

  6. de Wit, B., Herger, I., Samtleben, H.: Gauged locally supersymmetric D = 3 nonlinear sigma models. Nucl. Phys. B671, 175–216 (2003). hep-th/0307006

    Google Scholar 

  7. de Wit, B., Nicolai, H.: Extended supergravity with local SO(5) invariance. Nucl. Phys. B188, 98–108 (1981)

    Google Scholar 

  8. de Wit, B., Nicolai, H.: N=8 supergravity. Nucl. Phys. B208, 323–364 (1982)

    Google Scholar 

  9. de Wit, B., Samtleben, H., Trigiante, M.: On Lagrangians and gaugings of maximal supergravities. Nucl. Phys. B655, 93–126 (2003). hep-th/0212239

    Google Scholar 

  10. de Wit, B., Tollstén, A.K., Nicolai, H.: Locally supersymmetric D=3 nonlinear sigma models. Nucl. Phys. B392, 3–38 (1993). hep-th/9208074

    Google Scholar 

  11. Fischbacher, T.: Some stationary points of gauged N=16 D=3 supergravity. Nucl. Phys. B638, 207–219 (2002). hep-th/0201030

  12. Fischbacher, T.: Mapping the vacuum structure of gauged maximal supergravities: An application of high-performance symbolic algebra. PhD thesis 2003. hep-th/0305176

  13. Freedman, D.Z., Das, A.: Gauge internal symmetry in extended supergravity. Nucl. Phys. B120, 221 (1977)

  14. Freedman, D.Z., Schwarz, J.H.: N=4 supergravity theory with local SU(2) × SU(2) invariance. Nucl. Phys. B137, 333 (1978)

    Google Scholar 

  15. Fischbacher, T., Nicolai, H., Samtleben, H.: Vacua of maximal gauged D = 3 supergravities. Class. Quant. Grav. 19, 5297–5334 (2002). hep-th/0207206

    Article  MathSciNet  MATH  Google Scholar 

  16. Gibbons, G.W., Hull, C.M., Warner, N.P.: The stability of gauged supergravity. Nucl. Phys. B218, 173 (1983)

  17. Gukov, S.: Three-dimensional quantum gravity, Chern-Simons theory, and the A-polynomial 2003. hep-th/0306165

  18. Hull, C.M.: Noncompact gaugings of N=8 supergravity. Phys. Lett. B142, 39–41 (1984)

    Google Scholar 

  19. Hull, C.M.: More gaugings of N=8 supergravity. Phys. Lett. B148, 297–300 (1984)

    Google Scholar 

  20. Hull, C.M.: A new gauging of N=8 supergravity. Phys. Rev. D30, 760 (1984)

    Google Scholar 

  21. Hull, C.M.: New gauged N = 8, D = 4 supergravities 2002. hep-th/0204156

  22. Julia, B.: Application of supergravity to gravitation theories. In: Sabbata, V.D., Schmutzer, E. (eds.) Unified field theories in more than 4 dimensions, Singapore: World Scientific, 1983, pp. 215–236

  23. Koepsell, K., Nicolai, H., Samtleben, H.: An exceptional geometry for D=11 supergravity? Class. Quant. Grav. 17, 3689–3702 (2000). hep-th/0006034

    Article  MathSciNet  MATH  Google Scholar 

  24. Lu, H., Pope, C.N., Townsend, P.K.: Domain walls from anti-de Sitter spacetime. Phys. Lett. B391, 39–46 (1997). hep-th/9607164

    Google Scholar 

  25. Marcus, N., Schwarz, J.H.: Three-dimensional supergravity theories. Nucl. Phys. B228, 145–162 (1983)

    Google Scholar 

  26. Morales, J.F., Samtleben, H.: Supergravity duals of matrix string theory. JHEP 08, 042 (2002). hep-th/0206247

    Article  Google Scholar 

  27. Nicolai, H., Samtleben, H.: Maximal gauged supergravity in three dimensions. Phys. Rev. Lett. 86, 1686–1689 (2001). hep-th/0010076

    Article  MathSciNet  Google Scholar 

  28. Nicolai, H., Samtleben, H.: Compact and noncompact gauged maximal supergravities in three dimensions. JHEP 0104, 022 (2001). hep-th/0103032

    Google Scholar 

  29. Nicolai, H., Samtleben, H.: N = 8 matter coupled AdS3 supergravities. Phys. Lett. B514, 165–172 (2001). hep-th/0106153

  30. Nicolai, H., Samtleben, H.: Chern-Simons vs. Yang-Mills gaugings in three dimensions. Nucl. Phys. B668, 167–178 (2003). hep-th/0303213

    Google Scholar 

  31. Rosenfeld, B.: Geometry of Lie groups, Vol. 393 of Mathematics and its Applications. Dordrecht: Kluwer Academic Publishers Group, 1997

  32. Witten, E.: Quantization of Chern-Simons gauge theory with complex gauge group. Commun. Math. Phys. 137, 29–66 (1991)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Mühlenberg 1, 14476, Potsdam, Germany

    T. Fischbacher & H. Nicolai

  2. Institute for Theoretical Physics & Spinoza Institute, Utrecht University, Postbus 80.195, 3508, TD Utrecht, The Netherlands

    H. Samtleben

Authors
  1. T. Fischbacher
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Nicolai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Samtleben
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. Nicolai.

Additional information

Communicated by G.W. Gibbons

This work is partly supported by EU contract HPRN-CT-2000-00122 and HPRN-CT-2000-00131.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fischbacher, T., Nicolai, H. & Samtleben, H. Non-Semisimple and Complex Gaugings of N=16 Supergravity. Commun. Math. Phys. 249, 475–496 (2004). https://doi.org/10.1007/s00220-004-1081-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00220-004-1081-z

Keywords

Search

Navigation