Modifying the sum over topological sectors and constraints on supergravity

Article

Abstract

The standard lore about the sum over topological sectors in quantum field theory is that locality and cluster decomposition uniquely determine the sum over such sectors, thus leading to the usual θ-vacua. We show that without changing the local degrees of freedom, a theory can be modified such that the sum over instantons should be restricted; e.g. one should include only instanton numbers which are divisible by some integer p. This conclusion about the configuration space of quantum field theory allows us to carefully reconsider the quantization of parameters in supergravity. In particular, we show that FI-terms and nontrivial Kähler forms are quantized. This analysis also leads to a new derivation of recent results about linearized supergravity.

Keywords

Solitons Monopoles and Instantons Gauge Symmetry Discrete and Finite Symmetries Supergravity Models 

References

  1. [1]
    Z. Komargodski and N. Seiberg, Comments on the Fayet-Iliopoulos term in field theory and supergravity, JHEP 06 (2009) 007 [arXiv:0904.1159] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  2. [2]
    Z. Komargodski and N. Seiberg, Comments on supercurrent multiplets, supersymmetric field theories and supergravity, JHEP 07 (2010) 017 [arXiv:1002.2228] [SPIRES].CrossRefGoogle Scholar
  3. [3]
    D.Z. Freedman, Supergravity with axial gauge invariance, Phys. Rev. D 15 (1977) 1173 [SPIRES].ADSGoogle Scholar
  4. [4]
    R. Barbieri, S. Ferrara, D.V. Nanopoulos and K.S. Stelle, Supergravity, R invariance and spontaneous supersymmetry breaking, Phys. Lett. B 113 (1982) 219 [SPIRES].ADSGoogle Scholar
  5. [5]
    R. Kallosh, L. Kofman, A.D. Linde and A. Van Proeyen, Superconformal symmetry, supergravity and cosmology, Class. Quant. Grav. 17 (2000) 4269 [Erratum ibid. 21 (2004) 5017] [hep-th/0006179] [SPIRES].MATHCrossRefADSGoogle Scholar
  6. [6]
    G. Dvali, R. Kallosh and A. Van Proeyen, D-term strings, JHEP 01 (2004) 035 [hep-th/0312005] [SPIRES].CrossRefADSGoogle Scholar
  7. [7]
    K.R. Dienes and B. Thomas, On the inconsistency of Fayet-Iliopoulos terms in supergravity theories, Phys. Rev. D 81 (2010) 065023 [arXiv:0911.0677] [SPIRES].ADSGoogle Scholar
  8. [8]
    S.M. Kuzenko, The Fayet-Iliopoulos term and nonlinear self-duality, Phys. Rev. D 81 (2010) 085036 [arXiv:0911.5190] [SPIRES].ADSGoogle Scholar
  9. [9]
    S.M. Kuzenko, Variant supercurrent multiplets, JHEP 04 (2010) 022 [arXiv:1002.4932] [SPIRES]. CrossRefGoogle Scholar
  10. [10]
    E. Witten and J. Bagger, Quantization of Newton’s constant in certain supergravity theories, Phys. Lett. B 115 (1982) 202 [SPIRES].MathSciNetADSGoogle Scholar
  11. [11]
    G. Girardi, R. Grimm, M. Muller and J . Wess, Antisymmetric tensor gauge potential in curved superspace and a (16 + 16) supergravity multiplet, Phys. Lett. B 147 (1984) 81 [SPIRES].ADSGoogle Scholar
  12. [12]
    W. Lang, J. Louis and B.A. Ovrut, (16+ 16) supergravity coupled to matter: the low-energy limit of the superstring, Phys. Lett. B 158 (1985) 40 [SPIRES].ADSGoogle Scholar
  13. [13]
    W. Siegel, 16/16 supergravity, Class. Quant. Grav. 3 (1986) L47 [SPIRES].CrossRefADSGoogle Scholar
  14. [14]
    M. Dine, N. Seiberg and E. Witten, Fayet-Iliopoulos terms in string theory, Nucl. Phys. B 289 (1987) 589 [SPIRES]. CrossRefMathSciNetADSGoogle Scholar
  15. [15]
    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 [SPIRES]. CrossRefMathSciNetADSGoogle Scholar
  16. [16]
    S. Ashok and M.R. Douglas, Counting flux vacua, JHEP 01 (2004) 060 [hep-th/0307049] [SPIRES]. CrossRefMathSciNetADSGoogle Scholar
  17. [17]
    S.R. Coleman, More about the massive Schwinger model, Ann. Phys. 101 (1976) 239 [SPIRES].CrossRefADSGoogle Scholar
  18. [18]
    T. Banks, M. Dine and N. Seiberg, Irrational axions as a solution of the strong CP problem in an eternal universe, Phys. Lett. B 273 (1991) 105 [hep-th/9109040] [SPIRES].ADSGoogle Scholar
  19. [19]
    G.T. Horowitz, Exactly soluble diffeomorphism invariant theories, Commun. Math. Phys. 125 (1989) 417 [SPIRES]. MATHCrossRefMathSciNetADSGoogle Scholar
  20. [20]
    T. Pantev and E. Sharpe, Notes on gauging noneffective group actions, hep-th/0502027 [SPIRES].
  21. [21]
    T. Pantev and E. Sharpe, GLSM’s for gerbes (and other toric stacks), Adv. Theor. Math. Phys. 10 (2006) 77 [hep-th/0502053] [SPIRES].MATHMathSciNetGoogle Scholar
  22. [22]
    A. Caldararu, J. Distler, S. Hellerman, T. Pantev and E. Sharpe, Non-birational twisted derived equivalences in abelian GLSMs, Commun. Math. Phys. 294 (2010) 605 [arXiv:0709.3855] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  23. [23]
    E. Witten, unpublished.Google Scholar
  24. [24]
    J. Distler and B. Wecht, unpublished, mentioned in http://golem.ph.utexas.edu/∼distler/blog/archives/002180.html.
  25. [25]
    A.H. Chamseddine and H.K. Dreiner, Anomaly free gauged R symmetry in local supersymmetry, Nucl. Phys. B 458 (1996) 65 [hep-ph/9504337] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  26. [26]
    D.J. Castano, D.Z. Freedman and C. Manuel, Consequences of supergravity with gauged U(1)R symmetry, Nucl. Phys. B 461 (1996) 50 [hep-ph/9507397] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  27. [27]
    P. Binetruy, G. Dvali, R. Kallosh and A. Van Proeyen, Fayet-Iliopoulos terms in supergravity and cosmology, Class. Quant. Grav. 21 (2004) 3137 [hep-th/0402046] [SPIRES].MATHCrossRefADSGoogle Scholar
  28. [28]
    H. Elvang, D.Z. Freedman and B. Körs, Anomaly cancellation in supergravity with Fayet-Iliopoulos couplings, JHEP 11 (2006) 068 [hep-th/0606012] [SPIRES].CrossRefADSGoogle Scholar
  29. [29]
    T. Kugo and T.T. Yanagida, Coupling supersymmetric nonlinear σ-models to supergravity, arXiv:1003.5985 [SPIRES].
  30. [30]
    V.P. Akulov, D.V. Volkov and V.A. Soroka, On the general covariant theory of calibrating poles in superspace, Theor. Math. Phys. 31 (1977) 285 [Teor. Mat. Fiz. 31 (1977) 12] [SPIRES]. CrossRefMathSciNetGoogle Scholar
  31. [31]
    M.F. Sohnius and P.C. West, An alternative minimal off-shell version of N = 1 supergravity, Phys. Lett. B 105 (1981) 353 [SPIRES]. ADSGoogle Scholar
  32. [32]
    N.D. Lambert and G.W. Moore, Distinguishing off-shell supergravities with on-shell physics, Phys. Rev. D 72 (2005) 085018 [hep-th/0507018] [SPIRES].MathSciNetADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.School of Natural SciencesInstitute for Advanced StudyPrincetonU.S.A.

Personalised recommendations