arXiv:1012.5153v5 [hep-th] 23 Mar 2012 March 2011 New higher-derivative couplings in 4DN= 2 supergravity Daniel Butter and Sergei M. Kuzenko School of Physics M013, The University of Western Australia 35 Stirling Highway, Crawley W.A. 6009, Australia dbutter, kuzenko@cyllene.uwa.edu.au Abstract Using the off-shell formulation for generalN= 2 supergravity-matter sys- tems developed in arXiv:0905.0063, we propose a construction to generate a restricted chiral superfield from any real weight-zero projective multipletL. One can chooseLto be composed of tensor multiplets,O(2n) multiplets, with n= 2,3, . . ., and polar hypermultiplets. In conjunction with the standard pro- cedure to induce aN= 2 linear multiplet from any chiral weight-one scalar, we obtain a powerful mechanism to generate higher-derivative couplings in super- gravity. In the case thatLis a homogeneous function ofntensor multiplets of degree zero, we show that our construction is equivalent to that developed by de Wit and Saueressig in arXiv:hep-th/0606148 using the component supercon- formal tensor calculus. We also work out nontrivial examples withLcomposed ofO(2n) and tensor multiplets.
Contents 1Introduction1 2Main construction5 3The improved tensor multiplet7 3.1Evaluation of the contour integral . . . . . . . . . . . . . . . . . . . .7 3.2Super-Weyl gauge fixing with a tensor multiplet. . . . . . . . . . . .9 4Self-interacting tensor multiplets12 5AddingO(2n)multiplets14 5.1The case of a singleO(2n) multiplet. . . . . . . . . . . . . . . . . .14 5.2Generalization to severalO(2n) multiplets. . . . . . . . . . . . . . .17 6Discussion18 AGeometry of conformal supergravity23 BChiral projection operator25 CIsotwistors and projective superspace26 DContour integrals inCP127 EPrepotential formulations for vector multiplet30 1Introduction Recently, an off-shell formulation for generalN= 2 supergravity-matter couplings in four space-time dimensions has been constructed [1, 2, 3].It is a curved-space extension of the superconformal projective multiplets and their couplings [4] in 4D N= 2 projective superspace [5, 6, 7]. In the present paper, we will demonstrate that the methods developed in [1, 2, 3] and closely related works [8, 9] allow us to generate 1
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