N=2 Supersymmetric Gauge Theories with Nonpolynomial Interactions

Chapter 2
The Vector-Tensor Multiplet
The discovery of the vector-tensor multiplet by Sohnius, Stelle and West [9] dates back
to the year 1980, yet our current knowledge about its various incarnations and possible
interactions has been gathered only in the last three years. Its renaissance was triggered
by the work of de Wit et al. [10] on N = 2 supersymmetric vacua of heterotic string
theory compactified on K3 × T 2 . The massless states in this theory comprise a vector
and an antisymmetric tensor along with the dilaton, which organizes the perturbative
expansion of a string theory. These three fields could be shown to fit into a vectortensor
multiplet. In string theory, an antisymmetric tensor is usually dualized into a
pseudo-scalar, the axion, which in the case at hand results in an abelian N = 2 vector
multiplet, whose couplings have been studied extensively. However, not every vector
multiplet can be converted into a vector-tensor multiplet (see [11] for details), which
experiences much more stringent restrictions on its couplings. In any case, the duality
transformation can be performed only on-shell, for the off-shell structure of the two
multiplets is considerably different: the supersymmetry algebra of the vector-tensor
multiplet contains a central charge in addition to the gauge transformations that are
always present when gauge fields are involved.
The rediscovery of the vector-tensor multiplet spawned a lot of activity in this field.
In [12] the superfield for the free multiplet was constructed for the first time, which
subsequently could be generalized to include Chern-Simons couplings to nonabelian
vector multiplets [13, 14]. In [15] an alternative formulation utilizing the harmonic
superspace approach was presented. Already somewhat earlier, the central charge of the
multiplet was gauged in [16, 17] as a preparatory step towards a coupling to supergravity
(later achieved in [18], see also [19]), where the corresponding transformations would
necessarily have to be realized locally. In the course of this, a second variant of the
multiplet was discovered with nonlinear transformation laws, which give rise to selfinteractions.
These results were obtained by means of the so-called superconformal
multiplet calculus, yet their complexity called for a formulation in terms of superfields.
While in [20, 21] the nonlinear vector-tensor multiplet with rigid central charge could
be derived from a set of superfield constraints in harmonic superspace, the problem
of finding appropriate constraints describing the linear vector-tensor multiplet with
gauged central charge was first tackled by Dragon and the author in conventional
superspace [22, 23]. Finally, a general formalism for theories with gauged central charge
was developed in [2], again employing the virtues of harmonic superspace, and a natural
interpretation of the central charge of the linear vector-tensor multiplet as a remnant
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