$SU(4)$ harmonic superspace and supersymmetric gauge theory
B. M. Zupnik Joint Institute for Nuclear Research, Dubna, Moscow Oblast,
Russia
Abstract:
We consider the harmonic superspace formalism in
$N=4$ supersymmetry based on
$SU(4)/SU(2)\times SU(2)\times U(1)$ harmonics, which was previously used in Abelian gauge theory. We propose a transformation of non-Abelian constraints in the standard
$N{=}4$ superspace into a superfield equation for two basic analytic superfields: an independent strength
$W$ of dimension one and a dimensionless harmonic four-prepotential
$V$ of the
$U(1)$ charge two. These constraint equations I explicitly depend on the Grassmann coordinates
$\theta$, although they are covariant under nonstandard
$N=4$ supersymmetry transformations. The component expansion of superfield equations I generates the known equations for physical fields of the
$N=4$ supermultiplet, with the auxiliary fields vanishing or expressible in terms of physical fields on the mass shell. In the harmonic formalism of
$N=4$ supergauge theory off the mass shell, we construct a gauge-invariant action
$A(W,V)$ for two unconstrained non-Abelian analytic superfields
$W$ and
$V$; this action contains theta factors in each term and is invariant under the
$SU(4)$ automorphism group and scaling transformations. At the level of component fields, this model acquires an interaction of two infinite-dimensional
$N=4$ supermultiplets involving physical and auxiliary fields. The action
$A(W,V)$ generates analytic equations of motion II, alternative to the superfield constraints I. Both sets of equations give equivalent equations for physical component fields of the
$N=4$ gauge supermultiplet. We construct a nonlinear effective interaction for the Abelian harmonic superfield
$W$.
Keywords:
harmonic superspace, extended supersymmetry, Yang–Mills theory. Received: 30.06.2014
Revised: 06.02.2015
DOI:
10.4213/tmf8754