Instanton Effects in Three-Dimensional Supersymmetric Gauge Theories with Matter

Using standard field theory techniques we compute perturbative and instanton contributions to the Coulomb branch of three-dimensional supersymmetric QCD with N=2 and N=4 supersymmetry and gauge group SU(2). For the N=4 theory with one massless flavor, we confirm the proposal of Seiberg and Witten that the Coulomb branch is the double-cover of the centered moduli space of two BPS monopoles constructed by Atiyah and Hitchin. Introducing a hypermultiplet mass term, we show that the asymptotic metric on the Coulomb branch coincides with the metric on Dancer's deformation of the monopole moduli space. For the N=2 theory with $N_f$ flavors, we compute the one-loop corrections to the metric and complex structure on the Coulomb branch. We then determine the superpotential including one-loop effects around the instanton background. These calculations provide an explicit check of several results previously obtained by symmetry and holomorphy arguments.Comment: 24 pages, Late

Superconformal hypermultiplets

We present theories of N=2 hypermultiplets in four spacetime dimensions that are invariant under rigid or local superconformal symmetries. The target spaces of theories with rigid superconformal invariance are (4n)-dimensional {\it special} hyper-K\"ahler manifolds. Such manifolds can be described as cones over tri-Sasakian metrics and are locally the product of a flat four-dimensional space and a quaternionic manifold. The latter manifolds appear in the coupling of hypermultiplets to N=2 supergravity. We employ local sections of an Sp$(n)\times{\rm Sp}(1)$ bundle in the formulation of the Lagrangian and transformation rules, thus allowing for arbitrary coordinatizations of the hyper-K\"ahler and quaternionic manifolds

Covariant Quantisation in the Antifield Formalism

In this thesis we give an overview of the antifield formalism and show how it must be used to quantise arbitrary gauge theories. The formalism is further developed and illustrated in several examples, including Yang-Mills theory, chiral $W_3$ and $W_{2,5/2}$ gravity, strings in curved backgrounds and topological field theories. All these models are characterised by their gauge algebra, which can be open, reducible, or even infinitly reducible. We show in detail how to perform the gauge fixing and how to compute the anomalies using Pauli-Villars regularisation and the heat kernel method. Finally, we discuss the geometrical structure of the antifield formalism.Comment: Latex, 151 pages, PhD thesis, KUleuven, December 1995 12 files compressed into thes.tar.g

Redefining B-twisted topological sigma models

A recently proposed variation on the usual procedure to perform the topological B-twist in rigid $N=2$ models is applied to the case of the $\sigma$ model on a K\"ahler manifold. This leads to an alternative description of Witten's topological $\sigma$ model, which allows for a proper BRST interpretation and ghost number assignement. We also show that the auxiliary fields, which are responsible for the off shell closure of the $N=2$ algebra, play an important role in our construction.Comment: one reference adde

Instanton Solutions for the Universal Hypermultiplet

We expand our previous analysis on fivebrane and membrane instanton solutions in the universal hypermultiplet, including near-extremal multi-centered solutions and mixed fivebrane-membrane charged instantons. The results are most conveniently described in terms of a double-tensor multiplet.Comment: Minor changes, clarification added. Contribution to the proceedings of the 36th International Symposium Ahrenshoop, August 200

The Batalin-Vilkovisky Formalism on Fermionic Kaehler Manifolds

We show that the Kaehler structure can be naturally incorporated in the Batalin-Vilkovisky formalism. The phase space of the BV formalism becomes a fermionic Kaehler manifold. By introducing an isometry we explicitly construct the fermionic irreducible hermitian symmetric space. We then give some solutions of the master equation in the BV formalism

Ultracold Superstrings in atomic boson-fermion mixtures

We propose a setup with ultracold atomic gases that can be used to make a nonrelativistic superstring in four spacetime dimensions. In particular, we consider for the creation of the superstring a fermionic atomic gas that is trapped in the core of a vortex in a Bose-Einstein condensate. We explain the required tuning of experimental parameters to achieve supersymmetry between the fermionic atoms and the bosonic modes describing the oscillations in the vortex position. Furthermore, we discuss the experimental consequences of supersymmetry.Comment: 4 pages, 4 figures; published versio

Order parameter fluctuations in the holographic superconductor

We investigate the effect of order parameter fluctuations in the holographic superconductor. In particular, using a fully backreacted bulk geometry, the intrinsic spectral functions of the order parameter in both the normal and the superconducting phase are computed. We also present a vector-like large-$N$ version of the Ginzburg-Landau model that accurately describes our long-wavelength results in both phases. The large-$N$ limit of the latter model explains why the Higgs mode and the second-sound mode are not present in the spectral functions. Our results indicate that the holographic superconductor describes a relativistic multi-component superfluid in the universal regime of the BEC-BCS crossover.Comment: 21 pages, 15 figures; version accepted for publicatio

Construction of topological field theories using BV

We discuss in detail the construction of topological field theories using the Batalin--Vilkovisky (BV) quantisation scheme. By carefully examining the dependence of the antibracket on an external metric, we show that differentiating with respect to the metric and the BRST charge do not commute in general. We introduce the energy momentum tensor in this scheme and show that it is BRST invariant, both for the classical and quantum BRST operators. It is antifield dependent, guaranteeing gauge independence. For topological field theories, this energy momentum has to be quantum BRST exact. This leads to conditions at each order in $\hbar$. As an example of this procedure, we consider topological Yang--Mills theory. We show how the reducible set of symmetries used in topological Yang--Mills can be recovered by means of trivial systems and canonical transformations. Self duality of the antighosts is properly treated by introducing an infinite tower of auxiliary fields. Finally, it is shown that the full energy momentum tensor is classically BRST exact in the antibracket sense.Comment: 15

Membrane and fivebrane instantons from quaternionic geometry

We determine the one-instanton corrections to the universal hypermultiplet moduli space coming both from Euclidean membranes and NS-fivebranes wrapping the cycles of a (rigid) Calabi-Yau threefold. These corrections are completely encoded by a single function characterizing a generic four-dimensional quaternion-Kahler metric without isometries. We give explicit solutions for this function describing all one-instanton corrections, including the fluctuations around the instanton to all orders in the string coupling constant. In the semi-classical limit these results are in perfect agreement with previous supergravity calculations