Generalized gaugings and the field-antifield formalism

  • Frederik Coomans
  • Jan De Rydt
  • Antoine Van Proeyen
Article

Abstract

We discuss the algebra of general gauge theories that are described by the embedding tensor formalism. We compare the gauge transformations dependent and independent of an invariant action, and argue that the generic transformations lead to an infinitely reducible algebra. We connect the embedding tensor formalism to the field-antifield (or Batalin-Vilkovisky) formalism, which is the most general formulation known for general gauge theories and their quantization. The structure equations of the embedding tensor formalism are included in the master equation of the field-antifield formalism.

Keywords

Gauge Symmetry Supergravity Models 

References

  1. [1]
    B. de Wit and H. Nicolai, N = 8 supergravity, Nucl. Phys. B 208 (1982) 323 [SPIRES].CrossRefADSGoogle Scholar
  2. [2]
    L.J. Romans, Massive N = 2a supergravity in ten-dimensions, Phys. Lett. B 169 (1986) 374 [SPIRES].MathSciNetADSGoogle Scholar
  3. [3]
    H. Nicolai and H. Samtleben, Maximal gauged supergravity in three dimensions, Phys. Rev. Lett. 86 (2001) 1686 [hep-th/0010076] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  4. [4]
    H. Nicolai and H. Samtleben, Compact and noncompact gauged maximal supergravities in three dimensions, JHEP 04 (2001) 022 [hep-th/0103032] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  5. [5]
    B. de Wit, H. Samtleben and M. Trigiante, On lagrangians and gaugings of maximal supergravities, Nucl. Phys. B 655 (2003) 93 [hep-th/0212239] [SPIRES].ADSGoogle Scholar
  6. [6]
    B. de Wit, H. Samtleben and M. Trigiante, The maximal D = 5 supergravities, Nucl. Phys. B 716 (2005) 215 [hep-th/0412173] [SPIRES].ADSGoogle Scholar
  7. [7]
    B. de Wit and H. Samtleben, Gauged maximal supergravities and hierarchies of nonabelian vector-tensor systems, Fortsch. Phys. 53 (2005) 442 [hep-th/0501243] [SPIRES].MATHCrossRefGoogle Scholar
  8. [8]
    B. de Wit, H. Samtleben and M. Trigiante, Magnetic charges in local field theory, JHEP 09 (2005) 016 [hep-th/0507289] [SPIRES].CrossRefGoogle Scholar
  9. [9]
    B. de Wit, H. Nicolai and H. Samtleben, Gauged supergravities, tensor hierarchies and M-theory, JHEP 02 (2008) 044 [arXiv:0801.1294] [SPIRES].CrossRefGoogle Scholar
  10. [10]
    B. de Wit and H. Samtleben, The end of the p-form hierarchy, JHEP 08 (2008) 015 [arXiv:0805.4767] [SPIRES].CrossRefGoogle Scholar
  11. [11]
    B. de Wit and M. van Zalk, Supergravity and M-theory, Gen. Rel. Grav. 41 (2009) 757 [arXiv:0901.4519] [SPIRES].MATHCrossRefADSGoogle Scholar
  12. [12]
    E.A. Bergshoeff, J. Hartong, O. Hohm, M. Huebscher and T. Ortín, Gauge theories, duality relations and the tensor hierarchy, JHEP 04 (2009) 123 [arXiv:0901.2054] [SPIRES].CrossRefADSGoogle Scholar
  13. [13]
    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] [SPIRES].MathSciNetADSGoogle Scholar
  14. [14]
    M. Henneaux, Lectures on the antifield-BRST formalism for gauge theories, Nucl. Phys. Proc. Suppl. 18A (1990) 47 [SPIRES].MATHCrossRefMathSciNetADSGoogle Scholar
  15. [15]
    J. Gomis, J. Paris and S. Samuel, Antibracket, antifields and gauge theory quantization, Phys. Rept. 259 (1995) 1 [hep-th/9412228] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  16. [16]
    J. De Rydt, T.T. Schmidt, M. Trigiante, A. Van Proeyen and M. Zagermann, Electric/magnetic duality for chiral gauge theories with anomaly cancellation, JHEP 12 (2008) 105 [arXiv:0808.2130] [SPIRES].CrossRefADSGoogle Scholar
  17. [17]
    I.A. Batalin and G.A. Vilkovisky, Existence theorem for gauge algebra, J. Math. Phys. 26 (1985) 172 [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  18. [18]
    J.M.L. Fisch and M. Henneaux, Homological perturbation theory and the algebraic structure of the antifield-antibracket formalism for gauge theories, Commun. Math. Phys. 128 (1990) 627 [SPIRES].MATHCrossRefMathSciNetADSGoogle Scholar
  19. [19]
    B.L. Voronov and I.V. Tyutin, Formulation of gauge theories of general form. I, Theor. Math. Phys. 50 (1982) 218 [SPIRES].CrossRefMathSciNetGoogle Scholar
  20. [20]
    S. Vandoren and A. Van Proeyen, Simplifications in Lagrangian BV quantization exemplified by the anomalies of chiral W 3 gravity, Nucl. Phys. B 411 (1994) 257 [hep-th/9306147] [SPIRES].CrossRefADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  • Frederik Coomans
    • 1
  • Jan De Rydt
    • 1
  • Antoine Van Proeyen
    • 1
  1. 1.Instituut voor Theoretische FysicaKatholieke Universiteit LeuvenLeuvenBelgium

Personalised recommendations