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Manifest supersymmetry and the ADHM construction of instantons
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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
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