8,122 research outputs found
Wilson surfaces and higher dimensional knot invariants
An observable for nonabelian, higher-dimensional forms is introduced, its
properties are discussed and its expectation value in BF theory is described.
This is shown to produce potential and genuine invariants of higher-dimensional
knots.Comment: 31 pages, 9 figure
Integral Invariants of 3-Manifolds
This note describes an invariant of rational homology 3-spheres in terms of
configuration space integrals which in some sense lies between the invariants
of Axelrod and Singer and those of Kontsevich.Comment: 39 pages, AMS-LaTeX, to appear in J. Diff. Geo
Black Holes and Cosmological Constant in Bosonic String Theory: Some Remarks
(some corrections in the semiclassical study and one reference added).Comment: 17 pages; PHYZZX; IFUM 450/F
Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model
General boundary conditions ("branes") for the Poisson sigma model are
studied. They turn out to be labeled by coisotropic submanifolds of the given
Poisson manifold. The role played by these boundary conditions both at the
classical and at the perturbative quantum level is discussed. It turns out to
be related at the classical level to the category of Poisson manifolds with
dual pairs as morphisms and at the perturbative quantum level to the category
of associative algebras (deforming algebras of functions on Poisson manifolds)
with bimodules as morphisms. Possibly singular Poisson manifolds arising from
reduction enter naturally into the picture and, in particular, the construction
yields (under certain assumptions) their deformation quantization.Comment: 21 pages, 2 figures; minor corrections, references updated; final
versio
Loop and Path Spaces and Four-Dimensional BF Theories: Connections, Holonomies and Observables
We study the differential geometry of principal G-bundles whose base space is
the space of free paths (loops) on a manifold M. In particular we consider
connections defined in terms of pairs (A,B), where A is a connection for a
fixed principal bundle P(M,G) and B is a 2-form on M. The relevant curvatures,
parallel transports and holonomies are computed and their expressions in local
coordinates are exhibited. When the 2-form B is given by the curvature of A,
then the so-called non-abelian Stokes formula follows.
For a generic 2-form B, we distinguish the cases when the parallel transport
depends on the whole path of paths and when it depends only on the spanned
surface. In particular we discuss generalizations of the non-abelian Stokes
formula. We study also the invariance properties of the (trace of the) holonomy
under suitable transformation groups acting on the pairs (A,B).
In this way we are able to define observables for both topological and
non-topological quantum field theories of the BF type. In the non topological
case, the surface terms may be relevant for the understanding of the
quark-confinement problem. In the topological case the (perturbative)
four-dimensional quantum BF-theory is expected to yield invariants of imbedded
(or immersed) surfaces in a 4-manifold M.Comment: TeX, 39 page
Observables in the equivariant A-model
We discuss observables of an equivariant extension of the A-model in the
framework of the AKSZ construction. We introduce the A-model observables, a
class of observables that are homotopically equivalent to the canonical AKSZ
observables but are better behaved in the gauge fixing. We discuss them for two
different choices of gauge fixing: the first one is conjectured to compute the
correlators of the A-model with target the Marsden-Weinstein reduced space; in
the second one we recover the topological Yang-Mills action coupled with
A-model so that the A-model observables are closed under supersymmetry.Comment: 16 pages; minor correction
Quantum Models of Black Hole Evaporation
The discovery of black-hole evaporation represented in many respects a
revolutionary event in scientific world; as such, in giving answers to open
questions, it gave rise to new problems part of which are still not resolved.
Here we want to make a brief review of such problems and examine some possible
solutions. Invited Talk at the "Workshop on String Theory, Quantum Gravity and
the Unification of the Fundamental Interactions" Rome, September 21-26Comment: 9 pages, ROM2F-92/6
Loop observables for BF theories in any dimension and the cohomology of knots
A generalization of Wilson loop observables for BF theories in any dimension
is introduced in the Batalin-Vilkovisky framework. The expectation values of
these observables are cohomology classes of the space of imbeddings of a
circle. One of the resulting theories discussed in the paper has only trivalent
interactions and, irrespective of the actual dimension, looks like a
3-dimensional Chern-Simons theory.Comment: 13 page
A Conformal Affine Toda Model of 2D Black Holes: A Quantum Study of the Evaporation End-Point
In this paper we reformulate the dilaton-gravity theory of Callan \etal\ as a
new effective conformal field theory which turns out to be a generalization of
the so-called -conformal affine Toda (CAT) theory studied some times ago
by Babelon and Bonora. We quantize this model, thus keeping in account the
dilaton-gravity quantum effects. We then implement a Renormalization Group
analysis to study the black hole thermodynamics and the final state of the
Hawking evaporation.Comment: 15 pages, phyzzx, ROM-2F-92-5
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