Advertisement

Moduli spaces in AdS 4 supergravity

  • Senarath de Alwis
  • Jan Louis
  • Liam McAllister
  • Hagen Triendl
  • Alexander WestphalEmail author
Open Access
Article

Abstract

We study the structure of the supersymmetric moduli spaces of \( \mathcal{N} \) = 1 and \( \mathcal{N} \) = 2 supergravity theories in AdS 4 backgrounds. In the \( \mathcal{N} \) = 1 case, the moduli space cannot be a complex submanifold of the Kähler field space, but is instead real with respect to the inherited complex structure. In \( \mathcal{N} \) = 2 supergravity the same result holds for the vector multiplet moduli space, while the hypermultiplet moduli space is a Kähler submanifold of the quaternionic-Kähler field space. These findings are in agreement with AdS/CFT considerations.

Keywords

Supergravity Models AdS-CFT Correspondence Global Symmetries 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    B.W. Keck, An Alternative Class of Supersymmetries, J. Phys. A 8 (1975) 1819 [INSPIRE].ADSMathSciNetGoogle Scholar
  2. [2]
    B. Zumino, Nonlinear Realization of Supersymmetry in de Sitter Space, Nucl. Phys. B 127 (1977) 189 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    B. de Wit and I. Herger, Anti-de Sitter supersymmetry, Lect. Notes Phys. 541 (2000) 79 [hep-th/9908005] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    B. de Wit, Supergravity, hep-th/0212245 [INSPIRE].
  5. [5]
    A. Adams, H. Jockers, V. Kumar and J.M. Lapan, N = 1 σ-models in AdS 4, JHEP 12 (2011) 042 [arXiv:1104.3155] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  6. [6]
    G. Festuccia and N. Seiberg, Rigid Supersymmetric Theories in Curved Superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    O. Aharony, M. Berkooz, D. Tong and S. Yankielowicz, Confinement in Anti-de Sitter Space, JHEP 02 (2013) 076 [arXiv:1210.5195] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    J. Wess and J. Bagger, Supersymmetry and supergravity, Princeton University Press, Princeton U.S.A., (1992).zbMATHGoogle Scholar
  9. [9]
    S.J. Gates, M.T. Grisaru, M. Roček and W. Siegel, Superspace Or One Thousand and One Lessons in Supersymmetry, hep-th/0108200 [INSPIRE].
  10. [10]
    T. Banks and L.J. Dixon, Constraints on String Vacua with Space-Time Supersymmetry, Nucl. Phys. B 307 (1988) 93 [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    L.F. Abbott and M.B. Wise, Wormholes and Global Symmetries, Nucl. Phys. B 325 (1989) 687 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    R. Kallosh, A.D. Linde, D.A. Linde and L. Susskind, Gravity and global symmetries, Phys. Rev. D 52 (1995) 912 [hep-th/9502069] [INSPIRE].ADSMathSciNetGoogle Scholar
  13. [13]
    T. Banks and N. Seiberg, Symmetries and Strings in Field Theory and Gravity, Phys. Rev. D 83 (2011) 084019 [arXiv:1011.5120] [INSPIRE].ADSGoogle Scholar
  14. [14]
    M.J. Bowick, S.B. Giddings, J.A. Harvey, G.T. Horowitz and A. Strominger, Axionic Black Holes and a Bohm-Aharonov Effect for Strings, Phys. Rev. Lett. 61 (1988) 2823 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    M.J. Bowick, Axionic Black Holes and Wormholes, Gen. Rel. Grav. 22 (1990) 137 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  16. [16]
    K.A. Intriligator and N. Seiberg, Lectures on supersymmetric gauge theories and electric-magnetic duality, Nucl. Phys. Proc. Suppl. 45BC (1996) 1 [hep-th/9509066] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    W. Lerche, Introduction to Seiberg-Witten theory and its stringy origin, Nucl. Phys. Proc. Suppl. 55B (1997) 83 [hep-th/9611190] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    L. Andrianopoli, M. Bertolini, A. Ceresole, R. D’Auria, S. Ferrara 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] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    B. de Wit, H. Samtleben and M. Trigiante, Magnetic charges in local field theory, JHEP 09 (2005) 016 [hep-th/0507289] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  20. [20]
    R. D’Auria and S. Ferrara, On fermion masses, gradient flows and potential in supersymmetric theories, JHEP 05 (2001) 034 [hep-th/0103153] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  21. [21]
    K. Hristov, H. Looyestijn and S. Vandoren, Maximally supersymmetric solutions of D = 4 N =2 gauged supergravity, JHEP 11 (2009) 115 [arXiv:0909.1743] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    J. Louis, P. Smyth and H. Triendl, Supersymmetric Vacua in N = 2 Supergravity, JHEP 08 (2012) 039 [arXiv:1204.3893] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    D.V. Alekseevsky and S. Marchiafava, Hermitian and Kähler submanifolds of a quaternionic Kähler manifold, Osaka J. Math. 38 (2001) 869.MathSciNetzbMATHGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Senarath de Alwis
    • 1
  • Jan Louis
    • 2
    • 3
  • Liam McAllister
    • 4
  • Hagen Triendl
    • 5
  • Alexander Westphal
    • 6
    Email author
  1. 1.UCB 390, Physics DepartmentUniversity of ColoradoBoulderUnited States
  2. 2.Fachbereich Physik der Universität HamburgHamburgGermany
  3. 3.Zentrum für Mathematische PhysikUniversität HamburgHamburgGermany
  4. 4.Department of PhysicsCornell UniversityIthacaUnited States
  5. 5.Theory Division, Physics Department, CERNGeneva 23Switzerland
  6. 6.Deutsches Elektronen-Synchrotron DESY, Theory GroupHamburgGermany

Personalised recommendations