Volume 147B, number 4,5 PHYSICS LETTERS 8 November 1984 SELF-INTERACTING TENSOR MULTIPLETS IN N = 2 SUPERSPACE Anders KARLHEDE, Ulf LINDSTROM Institute of Theoretical Physics, University of Stockholm, Vanadisvk'gen 9, S-113 46 Stockholm, Sweden and Martin ROCEK 1 Institute for Theoretical Physics, State University of New York, Stony Brook, NY 11794, USA Received 25 June 1984 We give the N = 2 superspaee action for serf-interacting tensor multiplets in four dimensions and discuss the relation to the harmonic superspace recently proposed by Galperin et al. Superspace formulations of extended theories are notoriously difficult to construct. In particular, as the number of anticommuting coordinates increases, the number of unphysical components in a superfield grows and the mass dimension of the measure increases while the dimensions of the physical fields remain un- changed. One remedy is to use constrained superflelds to remove unphysical components and integrations over subspaces to decrease the dimension of the mea- sure. The simplest example of such a subintegration is the chiral integral in N = 1 superspace. A chiral mea- sure can also be used forN = 2 Yang-Mills theory [1] but not for the self-interacting tensor multiplet [2]. In this note we present the action for the four dimen- sional self-interacting tensor multiplet in N = 2 super- space. We use a novel subintegration which appears to break SU(2) invariance. The invariance is restored by a further integration over an internal parameter. We briefly comment on the relation to the recently introduced harmonic superspace [3]. The N = 2 tensor multiplet [4] is described by a real super field-strength F~b which satisfies Bianchi identities: Cd(aDbaFc)d=o, cd(a~)b&FC)d=O. (1) 1 Supported in part by the US National Science Foundation under contract No. PHY 81-09110 A-01. 0370-2693/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) We use the conventions of refs. [5,6] : latin letters are SU(2) isospin indices and greek letters are two-com- ponent spinor indices. We also sometimes write iso- spinors in boldface. F is an isovector and hence Fll = -F 2. The constraints (1) are solved in terms of a chiral prepotential 4: F~b = i(C be D2ac cb - Cac ~)2bc ~ ) . (2) Since the dimension ofF is 1 and the full superspace measure has dimension 0, an action with a full super- space integration must either be nonlocal or involve the prepotential ~ explicitly [4,5]. We thus look for a subintegration;however, F is not chiral and hence the obvious chiral integration cannot be used. We construct an appropriate measure by the method used in two di- mensions for the N = 4 twisted chiral multiplet [7]. To write a lagrangian quadratic in the field-strength we need a measure with four spinor derivatives, e.g., ~2~2. This means that the lagrangian g has to be in- dependent of the corresponding orthogonal subspace, e.g., Vag = Akg = 0. We take as our starting point the explicit form of (1) (suppressing spinor indices on the derivatives): DIF12=0, D2FI=0 , 2DIF1-D2F2=0 , 2D2Fll+D1FI=0, ~IF1--0, ~2F2=0, 2D1Fll - D2F 1 = 0, 2D2F 1 + DIF2 = 0. (3) 297