Skip to main content
SpringerLink
Log in

Cosmological Einstein-Maxwell instantons and euclidean supersymmetry: beyond self-duality

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We construct new supersymmetric solutions to the Euclidean Einstein-Maxwell theory with a non-vanishing cosmological constant, and for which the Maxwell field strength is neither self-dual or anti-self-dual. We find that there are three classes of solutions, depending on the sign of the Maxwell field strength and cosmological constant terms in the Einstein equations which arise from the integrability conditions of the Killing spinor equation. The first class is a Euclidean version of a Lorentzian supersymmetric solution found in [1, 2]. The second class is constructed from a three dimensional base space which admits a hyper-CR Einstein-Weyl structure. The third class is the Euclidean Kastor-Traschen solution.

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. S.L. Cacciatori, D. Klemm, D.S. Mansi and E. Zorzan, All timelike supersymmetric solutions of N = 2, D = 4 gauged supergravity coupled to abelian vector multiplets, JHEP 05 (2008) 097 [arXiv:0804.0009] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  2. S.L. Cacciatori, M.M. Caldarelli, D. Klemm and D.S. Mansi, More on BPS solutions of N = 2, D = 4 gauged supergravity, JHEP 07 (2004) 061 [hep-th/0406238] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  3. G.W. Gibbons and C.M. Hull, A Bogomolny bound for general relativity and solitons in N = 2 supergravity, Phys. Lett. B 109 (1982) 190 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  4. K.P. Tod, All metrics admitting supercovariantly constant spinors, Phys. Lett. B 121 (1983) 241 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  5. M. Dunajski and S.A. Hartnoll, Einstein-Maxwell gravitational instantons and five dimensional solitonic strings, Class. Quant. Grav. 24 (2007) 1841 [hep-th/0610261] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. J.B. Gutowski and W.A. Sabra, Gravitational instantons and euclidean supersymmetry, Phys. Lett. B 693 (2010) 498 [arXiv:1007.2421] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  7. M. Dunajski, J. Gutowski, W. Sabra and P. Tod, Cosmological Einstein-Maxwell instantons and euclidean supersymmetry: anti-self-dual solutions, Class. Quant. Grav. 28 (2011) 025007 [arXiv:1006.5149] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  8. A.A. Belavin, A.M. Polyakov, A.S. Schwartz and Y.S. Tyupkin, Pseudoparticle solutions of the Yang-Mills equations, Phys. Lett. B 59 (1975) 85 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  9. M. Dunajski and P. Tod, Einstein-Weyl structures from hyperKahler metrics with conformal Killing vectors, Differ. Geom. Appl. 14 (2001) 39.

    Article  MathSciNet  MATH  Google Scholar 

  10. N. Hitchin, Complex manifolds and Einstein’s equations, in Twistor geometry and non-linear systems, H.D. Doebner et al. eds., Springer, U.S.A. (1982).

    Google Scholar 

  11. P. Jones and K.P. Tod, Minitwistor spaces and Einstein-Weyl spaces, Class. Quant. Grav. 2 (1985) 565.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. J. Gillard, U. Gran and G. Papadopoulos, The spinorial geometry of supersymmetric backgrounds, Class. Quant. Grav. 22 (2005) 1033 [hep-th/0410155] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. U. Gran, J. Gutowski and G. Papadopoulos, The spinorial geometry of supersymmetric IIB backgrounds, Class. Quant. Grav. 22 (2005) 2453 [hep-th/0501177] [SPIRES].

    Article  MathSciNet  MATH  Google Scholar 

  14. H.B. Lawson and M.L. Michelsohn, Spin geometry, Princeton University Press, U.S.A. (1989).

    MATH  Google Scholar 

  15. McKenzie Y. Wang, Parallel spinors and parallel forms, Ann. Global Anal. Geom. 7 (1989) 59.

    Article  MathSciNet  MATH  Google Scholar 

  16. F.R. Harvey, Spinors and calibrations, Academic Press, London U.K. (1990).

    MATH  Google Scholar 

  17. D. Klemm and E. Zorzan, All null supersymmetric backgrounds of N = 2, D = 4 gauged supergravity coupled to abelian vector multiplets, Class. Quant. Grav. 26 (2009) 145018 [arXiv:0902.4186] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  18. J. Grover et al., Gauduchon-Tod structures, Sim holonomy and de Sitter supergravity, JHEP 07 (2009) 069 [arXiv:0905.3047] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  19. J.B. Gutowski and W.A. Sabra, Solutions of minimal four dimensional de Sitter supergravity, Class. Quant. Grav. 27 (2010) 235017 [arXiv:0903.0179] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  20. J. Grover, J.B. Gutowski, C.A.R. Herdeiro and W. Sabra, HKT geometry and de Sitter supergravity, Nucl. Phys. B 809 (2009) 406 [arXiv:0806.2626] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  21. J. Grover, J.B. Gutowski and W. Sabra, Null half-supersymmetric solutions in five-dimensional supergravity, JHEP 10 (2008) 103 [arXiv:0802.0231] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  22. J. Gutowski and G. Papadopoulos, Heterotic black horizons, JHEP 07 (2010) 011 [arXiv:0912.3472] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  23. S. Detournay, D. Klemm and C. Pedroli, Generalized instantons in N = 4 super Yang-Mills theory and spinorial geometry, JHEP 10 (2009) 030 [arXiv:0907.4174] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  24. R. Bryant, Pseudo-Riemannian metrics with parallel spinor fields and vanishing Ricci tensor, in the proceedings of the Analyse Harmonique et Analyse sur les Varietes, May 31–June 4, Luminy, France (1999), math.DG/0004073.

  25. J.B. Gutowski and W.A. Sabra, Half-supersymmetric solutions in five-dimensional supergravity, JHEP 12 (2007) 025 [arXiv:0706.3147] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  26. D. Kastor and J.H. Traschen, Cosmological multi-black hole solutions, Phys. Rev. D 47 (1993) 5370 [hep-th/9212035] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  27. P. Gauduchon and K.P. Tod, Hyper-Hermitian metrics with symmetry, J. Geom. Phys. 25 (1998) 291.

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, U.K.

    M. Dunajski

  2. Department of Mathematics, King’s College London, Strand, London, WC2R 2LS, U.K.

    J. B. Gutowski

  3. Centre for Advanced Mathematical Sciences and Physics Department, American University of Beirut, Beirut, Lebanon

    W. A. Sabra

  4. The Mathematical Institute, Oxford University, 24-29 St Giles, Oxford, OX1 3LB, UK

    Paul Tod

Authors
  1. M. Dunajski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. B. Gutowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. W. A. Sabra
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Paul Tod
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. B. Gutowski.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dunajski, M., Gutowski, J.B., Sabra, W.A. et al. Cosmological Einstein-Maxwell instantons and euclidean supersymmetry: beyond self-duality. J. High Energ. Phys. 2011, 131 (2011). https://doi.org/10.1007/JHEP03(2011)131

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP03(2011)131

Keywords

Search

Navigation