Evgenyi A. Ivanov
On the Harmonic Superspace Geometry of (4,4) Supersymmetric Sigma Models with Torsion
Preprint series: ESI preprints

MSC:

81T30 String and superstring theories; other extended objects , See also {83E30}

32C11 Complex supergeometry, See also {14A22, 14M30, 58A50}

58A50 Supermanifolds and graded manifolds, See also {14A22,

Abstract: Starting with the dual action of
$(4,4)$ $2D$ twisted multiplets in the harmonic
superspace with two independent sets of $SU(2)$ harmonic variables, we
present its generalization which hopefully provides an off-shell
description of general $(4,4)$ supersymmetric sigma models with
torsion.
Like the action of the torsionless $(4,4)$ hyper-K\"ahler sigma models in the
standard harmonic superspace, it is characterized by
a number of superfield potentials. They depend on $n$ copies of
a triple of analytic harmonic $(4,4)$ superfields. As distinct from the
hyper-K\"ahler case, the potentials
prove to be severely constrained by the self-consistency condition which
stems from the commutativity of the left and right harmonic derivatives.
We show that for $n=1$ these constraints reduce the general action to that
of $(4,4)$ twisted multiplet,
while for $n\geq 2$ there exists a wide class of new
actions which cannot be written only via twisted multiplets.
Their most striking feature is the nonabelian and in general
nonlinear gauge invariance which
substitutes the abelian gauge symmetry of the dual action of twisted
multiplets and ensures the correct number of physical degrees of
freedom.
We conjecture that these actions describe sigma models with non-commuting
left and right complex structures on the bosonic target.

Keywords: hyper-Kaehler sigma model, torsion, supersymmetry