A Renormalized Supersymmetry in the Topological Yang-Mills Field Theory

We reconsider the algebraic BRS renormalization of Witten's topological Yang-Mills field theory by making use of a vector supersymmetry Ward identity which improves the finiteness properties of the model. The vector supersymmetric structure is a common feature of several topological theories. The most general local counterterm is determined and is shown to be a trivial BRS-coboundary.Comment: 18 pages, report REF. TUW 94-10 and UGVA-DPT 1994/07-85

BF Topological Theories and Infinitely Reducible Systems

We present a rigurous disscusion for abelian $BF$ theories in which the base manifold of the $U(1)$ bundle is homeomorphic to a Hilbert space. The theory has an infinte number of stages of reducibility. We specify conditions on the base manifold under which the covarinat quantization of the system can be performed unambiguously. Applications of the formulation to the superparticle and the supertstring are also discussed.Comment: 10 pages, Late

On Dijkgraaf-Witten Type Invariants

We explicitly construct a series of lattice models based upon the gauge group $Z_{p}$ which have the property of subdivision invariance, when the coupling parameter is quantized and the field configurations are restricted to satisfy a type of mod-$p$ flatness condition. The simplest model of this type yields the Dijkgraaf-Witten invariant of a $3$-manifold and is based upon a single link, or $1$-simplex, field. Depending upon the manifold's dimension, other models may have more than one species of field variable, and these may be based on higher dimensional simplices.Comment: 18 page

Cognition Without Construction: Kant, Maimon, and the Transcendental Philosophy of Mathematics

In the Critique of Pure Reason, Immanuel Kant takes the ostensive constructions characteristic of Euclidean-style demonstrations to be the paradigm of both mathematical proofs and synthetic a priori cognition in general. However, the development of calculus included a number of techniques for representing infinite series of sums or differences, which could not be represented with the direct geometrical demonstrations of the past. Salomon Maimon’s Essay on Transcendental Philosophy addresses precisely this disparity. Maimon, owing much to G. W. Leibniz, proposes that differentials of sensation achieve what Kantian constructions could not. More importantly, Maimon develops a kind of symbolic cognition that is not delimited by the constraint of the pure forms of intuition. The mind does not construct its objects, but constructs itself through inquiry into the real objects of thought

Birmingham’s Eastside story: making steps towards sustainability?

Sustainability has come to play a dominant discursive role in the UK planning system, particularly relating to urban regeneration. The purpose of this paper is to evaluate the role that sustainability plays in a major regeneration programme, known as Eastside, currently underway in Birmingham, the UK. That this £6 billion redevelopment is now widely talked about by such key players as Birmingham City Council and the Regional Development Agency, Advantage West Midlands, as having a central sustainability agenda points to the growing importance of the ideal of sustainability in planning and regeneration agendas. In this paper, we investigate in detail how and why sustainability has become part of the planning discourse for Eastside and critically evaluate what impact, if any, this is having on public policy decision-making

An Exact Black Hole Entropy Bound

We show that a Rademacher expansion can be used to establish an exact bound for the entropy of black holes within a conformal field theory framework. This convergent expansion includes all subleading corrections to the Bekenstein-Hawking term.Comment: 6 pages, Latex, v2 minor re-wording, additional reference, to appear in Phyical Review D (title changed in journal

A New Action Principle for Witten's Topological Field Theory

In this letter a new gauge invariant, metric independent action is introduced from which Witten's Topological Quantum Field Theory may be obtained after gauge fixing using standard BRST techniques. In our model the BRST algebra of transformations, under which the effective action is invariant, close off-shell in distintion with what occurs in the one proposed by Labastida and Pernici. Our approach provides the geometrical principle for the quantum theory. We also compare our results with an alternative formulation presented by Baulieu and Singer.Comment: 8 pages, SB/F-94-22

Quasinormal Modes and Black Hole Quantum Mechanics in 2+1 Dimensions

We explore the relationship between classical quasinormal mode frequencies and black hole quantum mechanics in 2+1 dimensions. Following a suggestion of Hod, we identify the real part of the quasinormal frequencies with the fundamental quanta of black hole mass and angular momentum. We find that this identification leads to the correct quantum behavior of the asymptotic symmetry algebra, and thus of the dual conformal field theory. Finally, we suggest a further connection between quasinormal mode frequencies and the spectrum of a set of nearly degenerate ground states whose multiplicity may be responsible for the Bekenstein-Hawking entropy.Comment: 8 pages, LaTeX; references added and corrected, introduction and conclusion slightly expande

Support of dS/CFT correspondence from perturbations of three dimensional spacetime

We discuss the relation between bulk de Sitter three-dimensional spacetime and the corresponding conformal field theory at the boundary, in the framework of the exact quasinormal mode spectrum. We show that the quasinormal mode spectrum corresponds exactly to the spectrum of thermal excitations of Conformal Field Theory at the past boundary I^-, together with the spectrum of the Conformal Field Theory at the future boundary I^+.Comment: minor changes, new version accepted for publication in PL

Gauge symmetry breaking on orbifolds

We discuss a new method for gauge symmetry breaking in theories with one extra dimension compactified on the orbifold S^1/Z_2. If we assume that fields and their derivatives can jump at the orbifold fixed points, we can implement a generalized Scherk-Schwarz mechanism that breaks the gauge symmetry. We show that our model with discontinuous fields is equivalent to another with continuous but non periodic fields; in our scheme localized lagrangian terms for bulk fields appear.Comment: 6 pages, 2 figures. Talk given at the XXXVIIth Rencontres de Moriond, "Electroweak interactions and unified theories", Les Arcs, France, 9-16 Mar 2002. Minor changes, one reference adde