Advertisement

Variant vector-tensor multiplets in supergravity: classification and component reduction

  • Joseph Novak
Article

Abstract

The recent paper arXiv:1205.6881 has developed superform formulations for two versions of the vector-tensor multiplet and their Chern-Simons couplings in fourdimensional \(\mathcal{N}=2\) conformal supergravity. One of them is the standard vector-tensor multiplet with the central charge gauged by a vector multiplet. The other is the variant vector-tensor multiplet with the property that its own one-form gauges the central charge. Here a more general setup is presented in which the known versions reside as special cases. Analysis of the setup demonstrates that under certain assumptions there are two distinct variants, corresponding to the two formulations in arXiv:1205.6881. This provides a classification scheme for vector-tensor multiplets.

We then show that our superspace description leads to an efficient means of deriving component actions in supergravity. The entire action including all fermionic terms is derived for the non-linear vector-tensor multiplet. This extends the results of de Wit et al. in hep-th/9710212, where only the bosonic sector appeared. Finally, the bosonic sector of the action for the variant vector-tensor multiplet is given.

Keywords

Extended Supersymmetry Superspaces Supergravity Models 

References

  1. [1]
    P. Fayet, Fermi-Bose Hypersymmetry, Nucl. Phys. B 113 (1976) 135 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    M. Sohnius, Supersymmetry and Central Charges, Nucl. Phys. B 138 (1978) 109 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    M. Sohnius, K. Stelle and P.C. West, Off-mass shell formulation of extended supersymmetric gauge theories, Phys. Lett. B 92 (1980) 123 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    M. Sohnius, K. Stelle and P.C. West, Dimensional reduction by legendre transformation generates off-shell supersymmetric Yang-Mills theories, Nucl. Phys. B 173 (1980) 127 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    M.F. Sohnius, K.S. Stelle and P.C. West, Representations of extended supersymmetry, in Superspace and Supergravity, S.W. Hawking and M. Roček eds., Cambridge University Press, Cambridge, U.K. (1981), pg. 283.Google Scholar
  6. [6]
    B. de Wit, V. Kaplunovsky, J. Louis and D. Lüst, Perturbative couplings of vector multiplets in N = 2 heterotic string vacua, Nucl. Phys. B 451 (1995) 53 [hep-th/9504006] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    B. Milewski, Superfield formulation of the N = 2 super Yang-Mills model with central charge, Phys. Lett. B 112 (1982) 148 [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    B. Milewski, N = 1 superspace formulation of N = 2 and N = 4 super Yang-Mills models with central charge, Nucl. Phys. B 217 (1983) 172 [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    P. Claus, B. de Wit, M. Faux, B. Kleijn, R. Siebelink and P. Termonia, The Vector-tensor supermultiplet with gauged central charge, Phys. Lett. B 373 (1996) 81 [hep-th/9512143] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    P. Claus, P. Termonia, B. de Wit and M. Faux, Chern-Simons couplings and inequivalent vector-tensor multiplets, Nucl. Phys. B 491 (1997) 201 [hep-th/9612203] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    P. Claus, B. de Wit, M. Faux, B. Kleijn, R. Siebelink and P. Termonia, N = 2 supergravity Lagrangians with vector-tensor multiplets, Nucl. Phys. B 512 (1998) 148 [hep-th/9710212] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    A. Hindawi, B.A. Ovrut and D. Waldram, Vector-tensor multiplet in N = 2 superspace with central charge, Phys. Lett. B 392 (1997) 85 [hep-th/9609016] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    R. Grimm, M. Hasler and C. Herrmann, The N = 2 vector-tensor multiplet, central charge superspace and Chern-Simons couplings, Int. J. Mod. Phys. A 13 (1998) 1805 [hep-th/9706108] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    I. Buchbinder, A. Hindawi and B.A. Ovrut, A Two form formulation of the vector-tensor multiplet in central charge superspace, Phys. Lett. B 413 (1997) 79 [hep-th/9706216] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    N. Dragon, S.M. Kuzenko and U. Theis, The Vector-tensor multiplet in harmonic superspace, Eur. Phys. J. C 4 (1998) 717 [hep-th/9706169] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    N. Dragon and S.M. Kuzenko, Selfinteracting vector-tensor multiplet, Phys. Lett. B 420 (1998) 64 [hep-th/9709088] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    E. Ivanov and E. Sokatchev, On nonlinear superfield versions of the vector tensor multiplet, Phys. Lett. B 429 (1998) 35 [hep-th/9711038] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  18. [18]
    N. Dragon, E. Ivanov, S. Kuzenko, E. Sokatchev and U. Theis, N = 2 rigid supersymmetry with gauged central charge, Nucl. Phys. B 538 (1999) 411 [hep-th/9805152] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  19. [19]
    S.M. Kuzenko and J. Novak, Vector-tensor supermultiplets in AdS and supergravity, JHEP 01 (2012) 106 [arXiv:1110.0971] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  20. [20]
    D. Butter and J. Novak, Component reduction in N = 2 supergravity: the vector, tensor and vector-tensor multiplets, JHEP 05 (2012) 115 [arXiv:1201.5431] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    J. Novak, Superform formulation for vector-tensor multiplets in conformal supergravity, JHEP 09 (2012) 060 [arXiv:1205.6881] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    L. Andrianopoli, R. D’Auria and L. Sommovigo, D = 4, N = 2 supergravity in the presence of vector-tensor multiplets and the role of higher p-forms in the framework of free differential algebras, Adv. Stud. Theor. Phys. 1 (2008) 561 [arXiv:0710.3107] [INSPIRE].MathSciNetGoogle Scholar
  23. [23]
    L. Andrianopoli, R. D’Auria, L. Sommovigo and M. Trigiante, D = 4, N = 2 Gauged Supergravity coupled to Vector-Tensor Multiplets, Nucl. Phys. B 851 (2011) 1 [arXiv:1103.4813] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  24. [24]
    S. Kuzenko, U. Lindström, M. Roček and G. Tartaglino-Mazzucchelli, 4D N = 2 Supergravity and Projective Superspace, JHEP 09 (2008) 051 [arXiv:0805.4683] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    S. Kuzenko, U. Lindström, M. Roček and G. Tartaglino-Mazzucchelli, On conformal supergravity and projective superspace, JHEP 08 (2009) 023 [arXiv:0905.0063] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    D. Butter, N = 2 Conformal Superspace in Four Dimensions, JHEP 10 (2011) 030 [arXiv:1103.5914] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  27. [27]
    U. Theis, New N = 2 supersymmetric vector tensor interaction, Phys. Lett. B 486 (2000) 443 [hep-th/0005044] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  28. [28]
    U. Theis, Nonlinear vector tensor multiplets revisited, Nucl. Phys. B 602 (2001) 367 [hep-th/0012096] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  29. [29]
    D. Butter, S.M. Kuzenko and J. Novak, The linear multiplet and ectoplasm, JHEP 09 (2012) 131 [arXiv:1205.6981] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    P. Breitenlohner and M.F. Sohnius, Superfields, auxiliary fields, and tensor calculus for N = 2 extended supergravity, Nucl. Phys. B 165 (1980) 483[INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  31. [31]
    B. de Wit, J. van Holten and A. Van Proeyen, Central charges and conformal supergravity, Phys. Lett. B 95 (1980) 51 [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    S.M. Kuzenko and S. Theisen, Correlation functions of conserved currents in N = 2 superconformal theory, Class. Quant. Grav. 17 (2000) 665 [hep-th/9907107] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  33. [33]
    A.S. Galperin, E.A. Ivanov, V.I. Ogievetsky and E.S. Sokatchev, Harmonic superspace, Cambridge University Press, Cambridge, U.K. (2001).MATHCrossRefGoogle Scholar
  34. [34]
    P.S. Howe, Supergravity in superspace, Nucl. Phys. B 199 (1982) 309 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  35. [35]
    S.J. Gates Jr., Ectoplasm has no topology: the Prelude, hep-th/9709104 [INSPIRE].
  36. [36]
    S.J. Gates Jr., Ectoplasm has no topology, Nucl. Phys. B 541 (1999) 615 [hep-th/9809056] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  37. [37]
    S.J. Gates Jr., M.T. Grisaru, M.E. Knutt-Wehlau and W. Siegel, Component actions from curved superspace: normal coordinates and ectoplasm, Phys. Lett. B 421 (1998) 203 [hep-th/9711151] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  38. [38]
    T. Voronov, Geometric integration theory on supermanifolds, Sov. Sci. Rev. C 9 (1992) 1.Google Scholar
  39. [39]
    M.F. Hasler, The Three form multiplet in N = 2 superspace, Eur. Phys. J. C 1 (1998) 729 [hep-th/9606076] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  40. [40]
    G. Akemann, R. Grimm, M. Hasler and C. Herrmann, N = 2 central charge superspace and a minimal supergravity multiplet, Class. Quant. Grav. 16 (1999) 1617 [hep-th/9812026] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  41. [41]
    R. Grimm, M. Sohnius and J. Wess, Extended Supersymmetry and Gauge Theories, Nucl. Phys. B 133 (1978) 275 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  42. [42]
    B. de Wit, J. van Holten and A. Van Proeyen, Transformation Rules of N = 2 Supergravity Multiplets, Nucl. Phys. B 167 (1980) 186 [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    E. Bergshoeff, M. de Roo and B. de Wit, Extended Conformal Supergravity, Nucl. Phys. B 182 (1981) 173 [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    B. de Wit, J. van Holten and A. Van Proeyen, Structure of N = 2 Supergravity, Nucl. Phys. B 184 (1981) 77 [Erratum ibid. B 222 (1983) 516] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    B. de Wit, P. Lauwers and A. Van Proeyen, Lagrangians of N = 2 Supergravity - Matter Systems, Nucl. Phys. B 255 (1985) 569 [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    B. de Wit, R. Philippe and A. Van Proeyen, The improved tensor multiplet in N = 2 supergravity, Nucl. Phys. B 219 (1983) 143 [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    I.L. Buchbinder and S.M. Kuzenko, Ideas and Methods of Supersymmetry and Supergravity or a Walk Through Superspace, IOP, Bristol, U.K. (1998).MATHGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.School of Physics M013The University of Western AustraliaCrawleyAustralia

Personalised recommendations