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Manifest supersymmetry and the ADHM construction of instantons.pdf

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Manifest supersymmetry and the ADHM construction of instantons

a r X i v : h e p - t h / 9 4 1 2 0 3 2 v 2 3 0 D e c 1 9 9 4 JHU-TIPAC-94021 BONN-TH-94-27 hepth@xxx/9412032 December 1994 Manifest supersymmetry and the ADHM construction of instantons A. Galperin Department of Physics and Astronomy Johns Hopkins University Baltimore, MD 21218, USA and E. Sokatchev Physikalishes Institut Universita?t Bonn Nu?allee 12, 53115 Bonn, Germany Abstract We present the (0, 4) superspace version of Witten’s sigma model construction for ADHM instantons. We use the harmonic superspace formalism, which exploits the three complex structures common to both (0, 4) supersymmetry and self-dual Yang- Mills theory. A novel feature of the superspace formulation is the manifest interplay between the ADHM construction and its twistor counterpart. 1 Introduction In a recent very interesting paper [1] Witten constructed a (0, 4) supersymmetric linear sigma model in two dimensions with a potential term with surprising properties. Under certain assumptions about the structure of the multiplets involved, the Yukawa couplings of the model were found to satisfy the ADHM equations of the instantons construction [2]. In the infrared regime the massless chiral fermions in the model turned out to be coupled to the instanton gauge field, obtained exactly in accord with the ADHM prescription. The fact that (0, 4) supersymmetry implies self-duality of the target-space gauge fields is not new (see, for instance, [3]). However, it is a very unexpected feature of Witten’s model that it requires couplings to instantons, i.e., self-dual gauge fields with finite action. Non-linear (0, 4) sigma models with potentials had been discussed before (see, e.g., [4],[5]) and the restrictions on the potential imposed by supersymmetry had been found. However, this had been done in the traditional way of [6]. There one starts with one supersymmetry and then tries to add three more. This approach breaks the intrinsic automorphism SO(4) ～ SU(2) × SU(2)′ of (0, 4) supersymmetry to