Conformal Field Theory Between Supersymmetry and Indecomposable Structures

This thesis considers conformal field theory in its supersymmetric extension as well as in its relaxation to logarithmic conformal field theory. Compactification of superstring theory on four-dimensional complex manifolds obeying the Calabi-Yau conditions yields the moduli space of N=(4,4) superconformal field theories with central charge c=6 which consists of two continuously connected subspaces. This thesis is concerned with the subspace of K3 compactifications which is not well known yet. In particular, we inspect the intersection point of the Z_2 and Z_4 orbifold subvarieties within the K3 moduli space, explicitly identify the two corresponding points on the subvarieties geometrically, and give an explicit isomorphism of the three conformal field theory models located at that point, a specific Z_2 and a Z_4 orbifold model as well as the Gepner model (2)^4. We also prove the orthogonality of the two subvarieties at the intersection point. This is the starting point for the programme to investigate generic points in K3 moduli space. We use the coordinate identification at the intersection point in order to relate the coordinates of both subvarieties and to explicitly calculate a geometric geodesic between the two subvarieties as well as its generator. A generic point in K3 moduli space can be reached by such a geodesic originating at a known model. We also present advances on the conformal field theoretic side of deformations along such a geodesic using conformal deformation theory. Since a consistent regularisation of the appearing deformation integrals has not been achieved yet, the completion of this programme is still an open problem. Moreover, we regard a relaxation of conformal field theory to logarithmic conformal field theory. The latter allows the indecomposable action of the L_0 Virasoro mode within a representation of the conformal symmetry. In particular, we study general augmented c_{p,q} minimal models which generalise the well-known (augmented) c_{p,1} model series. We calculate logarithmic nullvectors in both types of models. But most importantly, we investigate the low lying Virasoro representation content and fusion algebra of two general augmented c_{p,q} models, the augmented c_{2,3} = 0 model as well as the augmented Yang-Lee model at c_{2,5} = -22/5. These exhibit a much richer structure as the c_{p,1} models with indecomposable representations up to rank 3. We elaborate several of these new rank 3 representations in great detail and uncover astonishing features. Furthermore, we argue that irreducible representations corresponding to the Kac table domain of the proper minimal models cannot be included into the theory. In particular, the true vacuum representation is rather given by a rank 1 indecomposable but not irreducible subrepresentation of a rank 2 representation. We generalise these generic examples to give the representation content and the fusion algebra of general augmented c_{p,q} models as a conjecture. Finally, we open a new connection between logarithmic conformal field theory and quantum spin chains by relating some representations of the augmented c_{2,3} = 0 model to the representation content of a c=0 model which describes an XXZ quantum spin chain

On explicit results at the intersection of the Z_2 and Z_4 orbifold subvarieties in K3 moduli space

We examine the recently found point of intersection between the Z_2 and Z_4 orbifold subvarieties in the K3 moduli space more closely. First we give an explicit identification of the coordinates of the respective Z_2 and Z_4 orbifold theories at this point. Secondly we construct the explicit identification of conformal field theories at this point and show the orthogonality of the two subvarieties.Comment: Latex, 23 page

Twistfield Perturbations of Vertex Operators in the Z_2-Orbifold Model

We apply Kadanoff's theory of marginal deformations of conformal field theories to twistfield deformations of Z_2 orbifold models in K3 moduli space. These deformations lead away from the Z_2 orbifold sub-moduli-space and hence help to explore conformal field theories which have not yet been understood. In particular, we calculate the deformation of the conformal dimensions of vertex operators for p^2<1 in second order perturbation theory.Comment: Latex2e, 19 pages, 1 figur

Notes on Generalised Nullvectors in logarithmic CFT

In these notes we discuss the procedure how to calculate nullvectors in general indecomposable representations which are encountered in logarithmic conformal field theories. In particular, we do not make use of any of the restrictions which have been imposed in logarithmic nullvector calculations up to now, especially the quasi-primarity of all Jordan cell fields. For the quite well-studied c_{p,1} models we calculate examples of logarithmic nullvectors which have not been accessible to the older methods and recover the known representation structure. Furthermore, we calculate logarithmic nullvectors in the up to now almost unexplored general augmented c_{p,q} models and use these to find bounds on their possible representation structures.Comment: 27 pages, 3 figures; v2: Corrected two typos, added one reference to the conclusio

Umsetzung eines Innovationscontrollings in ERP-Systemen am Beispiel SAP R/3

Innovationen sind für Unternehmen, die erfolgreich sein wollen, in der heutigen Zeitunbedingt notwendig.Aus der Notwendigkeit, Innovationen hervorbringen zu können, leitet sich direkt dieFrage ab, was Unternehmen tun können, um die Fähigkeit dazu sicher zu stellen,vielleicht sogar planen zu können. Zahlreiche Studien und die Recherche in derFachliteratur zeigen, dass sich der sehr allgemeine Begriff der Innovationsfähigkeitauf so genannte kritische Erfolgsfaktoren, wie z.B. den Anteil des F&E-Budgets amUmsatz oder die durchschnittlichen Fortbildungstage pro Mitarbeiter innerhalb einesJahres, herunter brechen lässt.Trotz der Aufteilung in einzelne Faktoren bleibt die Bewertung der Innovationsfähigkeitaber ein kompliziertes und vor allem komplexes Thema. Daraus leitet sichdie Anforderung ab, diesen Vorgang zu automatisieren oder zumindest durch denEinsatz von Datenverarbeitung zu unterstützen.Da der Innovationsprozess nicht auf einen oder wenige Bereiche des Unternehmensreduziert werden können, bietet sich der Einsatz von ERP-Systemen als Grundlagefür eine ganzheitliche Betrachtung des Unternehmens an.Um die Bewertung der Innovationsfähigkeit unterstützen zu können, wird sie durchdie Entwicklung eines Ressourcenbasierten Ansatzes in zwei Schritte geteilt. Dieerste Komponente, in Form der Bereitstellung der notwendigen Einsatzfaktoren (Zeit,Qualifikation, Geld…), kann in ERP-Systemen abgebildet werden. Der darauffolgende Schritt der Mittelverwendung muss weiterhin ohne systemseitigeUnterstützung bewertet werden.Eine mögliche Umsetzung des Ansatzes wird durch die Beschreibung eines aufBasis dieser Arbeit entwickelten Controllingtools aufgezeigt. Hierzu werden dieeinzelnen Funktionen und die graphische Oberfläche des Tools erläutert. Darüberhinaus werden die zum entwickelten Ansatz passenden Datenquellen in SAP R/3identifiziert. Es werden dabei vor allem die Module HR und CO als Datenbasisherangezogen.Zur Unterstützung des Verständnisses wird eine mögliche Einbindung in diebetrieblichen Abläufe beschrieben. Dabei wird geklärt, welche Stellen imUnternehmen die nötigen Aufgaben und Verantwortungen übernehmen können.Außerdem wird die Anwendung des Controllingtools anhand eines fiktivenUnternehmens dargestellt.Es zeigt sich, dass ERP-Systeme nur bedingt in der Lage sind, die Güte desInnovationsprozesses ganzheitlich zu bewerten. Zu viele Erfolgsfaktoren beziehensich auf zwischenmenschliche Prozesse und/oder sind nur qualitativ messbar unddamit nicht in ERP-Systemen abzubilden. Durch die Zweiteilung derInnovationsfähigkeit besteht aber die Möglichkeit, mit der Mittelbereitstellung einenzentralen Aspekt des Innovationsprozesses nicht nur abzubilden, sondern über dieUnterstützung durch ERP-Systeme ohne großen Aufwand greifbar und damit auchplanbar zu machen. Nicht gewünschte Tendenzen im Verlauf der Ist-Werte dereinzelnen Erfolgsfaktoren können rechtzeitig erkannt und gegebenenfalls durchMaßnahmen korrigiert werden.Innovations are absolutely necessary for companies, which want to be successful in today’s economic environment. From the need for being able to create innovations, the question is derived what companies could do, to guarantee this ability or make it even able to schedule. Numerous studies and the inquest in the technical literature shows, that the very general term “innovative ability” could be broken down to so-called “critical factors for success”, e.g. the quotient of the budget for research an development and the turnover or the average days for retraining per employee in one year. Despite to the division in separate factors, the rating of the ability to create innovations stays complicated and primarily complex. Hence the demand for an automation of this activity is deduced. Or at least an assistance by the application of data handling. Due to the fact that the innovation process can not be reduced to one or few divisions of a company, the use of ERP systems is provided as a base for an integral perception. For assisting the rating of the innovative ability, it is parted in two steps by the development of a resource-based approach. The first element, in the form of the allocation of the necessary input factors (time, qualification, money…) can be reproduced in ERP systems. The following step, the application of the input factors, has to be rated furthermore without assistance of the system. A potential implementation of the approach is shown by the description of a controlling tool, which was developed on the base of this diploma thesis. For this the several functions and the user interface are explained. Moreover the data origins in SAP R/3 will be identified, adapted to the approach. There are primarily the modules HR and CO, which are consulted as data pool. For promoting the comprehension there is an description of a possible integration in operative workflow. Thereby it is cleared, which positions of the company could adopt the necessary duties and responsibilities. There is also a demonstration of the application of the controlling tool with a virtual company. It is incidental, that ERP systems have only conditional the ability, to rate the innovation process integrated. Too much of the factors for success correspond to interpersonal processes or/and are only measurable qualitative. By this they are not able to reproduce them in ERP systems. Though, via the dichotomy of the innovation ability, with the allocation of input factors, there is the possibility to reproduce one central aspect of the innovation process. Trough the assistance of ERP systems it is not only able to reproduce, but also to make it concrete und therewith able to schedule. Not designated tendencies in the actual values of the several success factors can be discovered timely and be adjusted by sanctions i