N=2 Supersymmetric Gauge Theories with Nonpolynomial Interactions

Abstract
In this thesis the central charge of the vector-tensor multiplet is gauged, giving rise
to N = 2 supersymmetric models in four dimensions which involve nonpolynomial yet
local couplings of 1-form gauge potentials to an antisymmetric tensor field.
Following an introduction to the N = 2 supersymmetry algebra with a local central
charge and a discussion of the massive Fayet-Sohnius hypermultiplet as a simple realisation,
we investigate deformations of the superfield constraints that determine the
vector-tensor multiplet. The supersymmetry and central charge transformations of its
tensor components as well as the Bianchi identities for the field strengths are given
for arbitrary consistent deformations, which facilitates the formulation of a particular
model. To verify the validity of a given constraint, we supply a set of consistency
conditions.
We then focus on the coupling to an abelian vector multiplet that gauges the central
charge. The consistency conditions yield a system of partial differential equations, and
two classes of solutions are presented which provide superfield constraints for both the
linear and the self-interacting vector-tensor multiplet.
With these as the foundation, we first consider the linear case. It is shown how the
particular structure of the Bianchi identities is responsible for the nonpolynomial central
charge transformations of the vector and antisymmetric tensor. From a general
prescription for the construction of invariant actions by means of a linear superfield we
derive the Lagrangian, whose nonpolynomial vector-tensor interactions turn out to fit
into the framework of new (nonsupersymmetric) gauge field theories found recently by
Henneaux and Knaepen, to which we provide an introduction.
The nonlinear version of the vector-tensor multiplet is investigated in the last chapter.
We explain in detail how the superfield constraints give rise to couplings of the
antisymmetric tensor to Chern-Simons forms of both the vector and the central charge
gauge field. We are unable, however, to construct a corresponding Henneaux-Knaepen
model.
Keywords: Supersymmetry, Gauge Theories, Central Charge