Abstract
We present most elements of tensor calculus for N = 2 extended (Poincaré) supergravity. Starting from the off-shell algebra with the minimal set of 32 + 32 field components, we study various types of abstract multiplets (linear, chiral, Yang-Mills, matter) and give an action formula for the linear as well as the chiral one. As an application, we construct invariant actions for super- gravity, an arbitrary Yang-Mills multiplet, a gauged non-trivial SU(2) and the matter (hyper) multiplet. We give the candidate for an invariant three-loop counterterm.
The work presented here was mostly done together with M. Sohnius and A. Kabelschacht; part of it is published1, other parts are prepared for publication2. Our work is closely related to that of Fradkin and Vasiliev3 and of De Roo, De Wit, van Holten and van Proeyen4.
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References
P. Breitenlohner and M.F. Sohnius, Nucl. Phys. B165 (1980) 483; P. Breitenlohner, in “Supergravity”, Proc. of the Supergravity workshop at Stony Brook, Sept. 1979, ed. by P. van Nieuwenhuizen and D.Z. Freedman (North Holland, Amsterdam, 1979) which also contains a fairly complete compilation of supergravity references; P. Breitenlohner, “Superfield Formulation, Auxiliary Fields and Tensor Calculus for supergravity”, presented at the 17th Winter School of Theoretical Physics, Feb. 22-March 6, 1980, Karpacz, Poland.
P. Breitenlohner and M.F. Sohnius, MP5 preprint, to appear (1980).
E.S. Fradkin and M.A. Vasiliev, Lett. Nuovo Cimento 25 (1979) 79; Phys. Letters 85B (1979) 47.
B. De Wit and J.W. van Hoi ten, Nucl. Phys. B155 (1979) 530; B. De Wit, in “Supergravity”, Ref. 1); B. De Wit, J.W. van Hoi ten and A. van Proeyen, Leuven preprint KUL-TF-79/034 (1979); M. De Roo, J.W. van Hoi ten, B. De Wit and A. van Proeyen, “Chiral Superfields in N = 2 Supergravity”, Leiden preprint (1980).
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A. van Proeyen, “N = 2 Supergravity Multiplets”, presented at the 17th Winter School of Theoretical Physics, Feb. 22-March 6, 1980, Karpacz, Poland.
D.Z. Freedman, Phys. Rev. D15 (1977) 1173; P. van Nieuwenhuizen and B. De Wit, Nucl. Phys. B139 (1978) 216.
P. Fayet, Nucl. Phys. B113 (1976) 135; C. Zachos, Phys. Letters 76B (1978) 329.
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Breitenlohner, P. (1980). Tensor Calculus for N = 2 Extended Supergravity. In: Ferrara, S., Ellis, J., van Nieuwenhuizen, P. (eds) Unification of the Fundamental Particle Interactions. Ettore Majorana International Science Series, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3171-1_18
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DOI: https://doi.org/10.1007/978-1-4613-3171-1_18
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