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Journal of High Energy Physics

, 2016:132 | Cite as

The anomalous current multiplet in 6D minimal supersymmetry

  • Sergei M. Kuzenko
  • Joseph Novak
  • Igor B. Samsonov
Open Access
Regular Article - Theoretical Physics
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Abstract

For supersymmetric gauge theories with eight supercharges in four, five and six dimensions, a conserved current belongs to the linear multiplet. In the case of sixdimensional \( \mathcal{N}=\left(1,\ 0\right) \) Poincaré supersymmetry, we present a consistent deformation of the linear multiplet which describes chiral anomalies. This is achieved by developing a superform formulation for the deformed linear multiplet. In the abelian case, we compute a nonlocal effective action generating the gauge anomaly.

Keywords

Superspaces Supersymmetric Effective Theories Anomalies in Field and String Theories 
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References

  1. [1]
    P. Breitenlohner and M.F. Sohnius, Superfields, auxiliary fields and tensor calculus for N = 2 extended supergravity, Nucl. Phys. B 165 (1980) 483 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  2. [2]
    E.I. Buchbinder, S.M. Kuzenko and I.B. Samsonov, Superconformal field theory in three dimensions: correlation functions of conserved currents, JHEP 06 (2015) 138 [arXiv:1503.04961] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  3. [3]
    E.I. Buchbinder, S.M. Kuzenko and I.B. Samsonov, Implications of \( \mathcal{N}=4 \) superconformal symmetry in three spacetime dimensions, JHEP 08 (2015) 125 [arXiv:1507.00221] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  4. [4]
    A. Salam and E. Sezgin, Supergravities in diverse dimensions, volume 2, World Scientific, Singapore (1989).Google Scholar
  5. [5]
    C. Arias, W.D. Linch, III and A.K. Ridgway, Superforms in simple six-dimensional superspace, arXiv:1402.4823 [INSPIRE].
  6. [6]
    P.S. Howe and A. Umerski, Anomaly multiplets in six-dimensions and ten-dimensions, Phys. Lett. B 198 (1987) 57 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  7. [7]
    P.S. Howe, K.S. Stelle and P.K. Townsend, The relaxed hypermultiplet: an unconstrained N =2 superfield theory,Nucl. Phys. B 214(1983) 519 [INSPIRE].CrossRefADSGoogle Scholar
  8. [8]
    P.S. Howe and E. Sezgin, Anomaly free tensor Yang-Mills system and its dual formulation, Phys. Lett. B 440 (1998) 50 [hep-th/9806050] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  9. [9]
    P.S. Howe, G. Sierra and P.K. Townsend, Supersymmetry in six-dimensions, Nucl. Phys. B 221 (1983) 331 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  10. [10]
    J. Koller, A six-dimensional superspace approach to extended superfields, Nucl. Phys. B 222 (1983) 319 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  11. [11]
    P.H. Frampton and T.W. Kephart, Explicit evaluation of anomalies in higher dimensions, Phys. Rev. Lett. 50 (1983) 1343 [Erratum ibid. 51 (1983) 232] [INSPIRE].
  12. [12]
    P.H. Frampton and T.W. Kephart, The analysis of anomalies in higher space-time dimensions, Phys. Rev. D 28 (1983) 1010 [INSPIRE].ADSGoogle Scholar
  13. [13]
    L. Álvarez-Gaumé and E. Witten, Gravitational anomalies, Nucl. Phys. B 234 (1984) 269 [INSPIRE].CrossRefADSGoogle Scholar
  14. [14]
    B. Zumino, Y.-S. Wu and A. Zee, Chiral anomalies, higher dimensions and differential geometry, Nucl. Phys. B 239 (1984) 477 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  15. [15]
    H. Leutwyler, Chiral fermion determinants and their anomalies, Phys. Lett. B 152 (1985) 78 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  16. [16]
    W.D. Linch, III and G. Tartaglino-Mazzucchelli, Six-dimensional supergravity and projective superfields, JHEP 08 (2012) 075 [arXiv:1204.4195] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  17. [17]
    D. Butter, S.M. Kuzenko and J. Novak, The linear multiplet and ectoplasm, JHEP 09 (2012) 131 [arXiv:1205.6981] [INSPIRE].CrossRefADSGoogle Scholar
  18. [18]
    L. Mezincescu, On the superfield formulation of O(2) supersymmetry, JINR-P2-12572 (1979).Google Scholar
  19. [19]
    I.A. Batalin and G.A. Vilkovisky, Quantization of gauge theories with linearly dependent generators, Phys. Rev. D 28 (1983) 2567 [Erratum ibid. D 30 (1984) 508] [INSPIRE].
  20. [20]
    J. Wess and B. Zumino, Consequences of anomalous Ward identities, Phys. Lett. B 37 (1971) 95 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  21. [21]
    P. Binetruy, G. Girardi and R. Grimm, Supergravity couplings: a geometric formulation, Phys. Rept. 343 (2001) 255 [hep-th/0005225] [INSPIRE].CrossRefADSMathSciNetMATHGoogle Scholar
  22. [22]
    A.S. Galperin, E.A. Ivanov, V.I. Ogievetsky and E.S. Sokatchev, Harmonic superspace, Cambridge University Press, Cambridge U.K. (2001).CrossRefMATHGoogle Scholar
  23. [23]
    I.L. Buchbinder, S.M. Kuzenko and B.A. Ovrut, On the D = 4, N = 2 nonrenormalization theorem, Phys. Lett. B 433 (1998) 335 [hep-th/9710142] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  24. [24]
    E.A. Ivanov, A.V. Smilga and B.M. Zupnik, Renormalizable supersymmetric gauge theory in six dimensions, Nucl. Phys. B 726 (2005) 131 [hep-th/0505082] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  25. [25]
    I.L. Buchbinder and N.G. Pletnev, Construction of 6D supersymmetric field models in N = (1,0) harmonic superspace,Nucl. Phys. B 892(2015) 21 [arXiv:1411.1848] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  26. [26]
    I.L. Buchbinder and N.G. Pletnev, Leading low-energy effective action in the 6D hypermultiplet theory on a vector/tensor background, Phys. Lett. B 744 (2015) 125 [arXiv:1502.03257] [INSPIRE].CrossRefADSGoogle Scholar
  27. [27]
    A. Galperin, E. Ivanov, S. Kalitsyn, V. Ogievetsky and E. Sokatchev, Unconstrained N = 2 Matter, Yang-Mills and supergravity theories in harmonic superspace, Class. Quant. Grav. 1 (1984) 469 [Erratum ibid. 2 (1985) 127] [INSPIRE].
  28. [28]
    U. Lindström and M. Roček, N = 2 super Yang-Mills theory in projective superspace, Commun. Math. Phys. 128 (1990) 191 [INSPIRE].CrossRefADSMATHGoogle Scholar
  29. [29]
    D. Butter and S.M. Kuzenko, New higher-derivative couplings in 4D N = 2 supergravity, JHEP 03 (2011) 047 [arXiv:1012.5153] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  30. [30]
    S.M. Kuzenko, Projective superspace as a double punctured harmonic superspace, Int. J. Mod. Phys. A 14 (1999) 1737 [hep-th/9806147] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  31. [31]
    P.S. Howe, K.S. Stelle and P.C. West, N = 1 D = 6 harmonic superspace, Class. Quant. Grav. 2 (1985) 815 [INSPIRE].CrossRefADSMathSciNetMATHGoogle Scholar
  32. [32]
    B.M. Zupnik, Six-dimensional supergauge theories in the harmonic superspace, Sov. J. Nucl. Phys. 44 (1986) 512 [Yad. Fiz. 44 (1986) 794] [INSPIRE].
  33. [33]
    B.M. Zupnik, The action of the supersymmetric N = 2 gauge theory in harmonic superspace, Phys. Lett. B 183 (1987) 175 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  34. [34]
    U. Lindström and M. Roček, New HyperKähler metrics and new supermultiplets, Commun. Math. Phys. 115 (1988) 21 [INSPIRE].CrossRefADSMATHGoogle Scholar
  35. [35]
    S.M. Kuzenko, Lectures on nonlinear σ-models in projective superspace, J. Phys. A 43 (2010) 443001 [arXiv:1004.0880] [INSPIRE].ADSMathSciNetGoogle Scholar
  36. [36]
    S.M. Kuzenko and G. Tartaglino-Mazzucchelli, N = 4 supersymmetric Yang-Mills theories in AdS 3, JHEP 05 (2014) 018 [arXiv:1402.3961] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  37. [37]
    D. Butter, S.M. Kuzenko, J. Novak and G. Tartaglino-Mazzucchelli, Conformal supergravity in five dimensions: new approach and applications, JHEP 02 (2015) 111 [arXiv:1410.8682] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  38. [38]
    A. Galperin, E.A. Ivanov, V. Ogievetsky and E. Sokatchev, Harmonic supergraphs. Green functions, Class. Quant. Grav. 2 (1985) 601 [INSPIRE].

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Sergei M. Kuzenko
    • 1
  • Joseph Novak
    • 2
  • Igor B. Samsonov
    • 1
  1. 1.School of Physics M013The University of Western AustraliaCrawleyAustralia
  2. 2.Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-InstitutGolmGermany

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