N=2 Supersymmetric Gauge Theories with Nonpolynomial Interactions

Introduction
Despite the lack of experimental hints, supersymmetry counts among the most popular
and promising concepts in theoretical high energy physics. It features prominently
both in quantum theories of point particles and of extended objects; in particular it is
a prerequisite to the formulation of realistic string theories, which are assumed to unify
the standard model of strong and electroweak forces with Einstein’s gravity.
Although less attractive from a phenomenological point of view, models with extended,
i.e. more than one, supersymmetry have provided much insight into nonperturbative
phenomena of quantum field theories as well as into various (mostly conjectured) dualities
between different superstring theories. N =2 supersymmetry in four dimensions
in particular has received great attention lately due to the seminal work of Seiberg and
Witten on N = 2 supersymmetric Yang-Mills theories. While these are usually formulated
in terms of vector multiplets, there exists another multiplet describing the same
kind of physical states, which trades one scalar for an antisymmetric tensor field. Such
multiplets with 2-form gauge potentials occur universally in string theories, and the
so-called vector-tensor multiplet especially has recently been shown to be part of the
massless spectrum of four-dimensional N = 2 supersymmetric heterotic string vacua.
It was this discovery that has renewed interest in the long known, yet largely ignored,
vector-tensor multiplet and its possible interactions, and in the present thesis we offer
a novel derivation of the most important results obtained on this subject in the last
three years.
An off-shell formulation of the multiplet requires the presence of a central charge in the
supersymmetry algebra, at least when only a finite number of components is desired.
This central charge generates an on-shell nontrivial global symmetry of a rather unusual
kind. It can be promoted to a local symmetry by coupling the vector-tensor multiplet
to an abelian vector multiplet that provides the gauge field for the local central charge
transformations. These and the couplings of the vector-tensor components in the invariant
action share the peculiar property of being nonpolynomial in the gauge field.
What at first had been considered a completely new type of gauge theory, turned out
to fit into a larger class of models found somewhat earlier by Henneaux and Knaepen
outside the framework of supersymmetry. In four dimensions, these bosonic models describe
consistent interactions of 1-form and 2-form gauge potentials, which in general
are nonpolynomial in both kinds of fields. While recently an N = 1 supersymmetric
formulation of all Henneaux-Knaepen models has been given by Brandt and the author,
so far all attempts to go beyond the vector-tensor multiplet in order to construct more
general HK models with two supersymmetries have been unsuccessful. On the other
hand, we are going to show that the vector-tensor multiplet itself suggests a possible
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