AdS-Flows and Weyl Gravity

An analogy is noted between RG flow equations in 4-dimensional gauge theory, as derived from the AdS/CFT correspondence, and the RG flow equations in 4-dimensional field theory coupled to a particular limit of Weyl supergravity. This suggests a possible theory of dynamical 3-branes with fluctuating 4-dimensional conformal factor. The argument involves a map from flows in 4-dimensional gauge theories to flows in a class of 2-dimensional sigma models.Comment: 25 pages Latex; some comments, references adde

Making the gravitational path integral more Lorentzian, or: Life beyond Liouville gravity

In two space-time dimensions, there is a theory of Lorentzian quantum gravity which can be defined by a rigorous, non-perturbative path integral and is inequivalent to the well-known theory of (Euclidean) quantum Liouville gravity. It has a number of appealing features: i) its quantum geometry is non-fractal, ii) it remains consistent when coupled to matter, even beyond the c=1 barrier, iii) it is closer to canonical quantization approaches than previous path-integral formulations, and iv) its construction generalizes to higher dimensions.Comment: 4 pages, 2 figures (postscript), uses espcrc2.st

Stability and integration over Bergman metrics

We study partition functions of random Bergman metrics, with the actions defined by a class of geometric functionals known as `stability functions'. We introduce a new stability invariant - the critical value of the coupling constant - defined as the minimal coupling constant for which the partition function converges. It measures the minimal degree of stability of geodesic rays in the space the Bergman metrics, with respect to the action. We calculate this critical value when the action is the $\nu$-balancing energy, and show that $\gamma_k^{\rm crit} = k - h$ on a Riemann surface of genus $h$.Comment: 24 pages, 3 figure

Complexity and maintenance : a comparative study of object-oriented and structured methodologies : a thesis presented in partial fulfilment of the requirements for the degree of Master of Business Studies in Information Systems at Massey University

Maintenance has been found to be one of the most expensive phases in the life of an information system. It has been suggested that the use of object-oriented methods instead of traditional structured methods may be one way of reducing the cost of maintenance required for an information system. This thesis is an attempt to determine whether the object-oriented approach does in fact undergo a relatively smaller increase in complexity when subjected to a change in specifications than a similar system that is developed using a "structured methodology", and is therefore easier to maintain. The methodologies used in this study were Yourdon's (1989) Modern Structured Methodology and Booch's (1994) Object-Oriented methodology. The analysis phase of both methodologies were applied to the same case study twice in order to evaluate the effects of a change in the system's specifications. Once the two models for each methodology were complete, various metrics were applied to the structured system and a separate set of metrics were applied to the object-oriented system. The results of the models and the metrics were then analysed and validated in order to determine which system suffered a smaller proportional increase in complexity as a result of the changes to the system. It was found that overall, the object-oriented system proved to undergo a smaller increase in complexity, and it was therefore easier to maintain as a result of the changes than the structured system