Related papers: Conformal and projective tractors from 2-frame bun…

The methods of conformal field theory are used to compute the crossing probabilities between segments of the boundary of a compact two-dimensional region at the percolation threshold. These probabilities are shown to be invariant not only…

The standard covariant differentiation procedure for fields in vector bundles is generalised so as to be applicable to fields in general nonaffine bundles in which the fibres may have an arbitrary nonlinear structure. In addition to the…

For a weak 2-group, we construct a bicategory of flat 2-group bundles over differentiable stacks as a localization of a functor bicategory. This description is amenable to explicit geometric constructions. For example, we show that flat…

In this paper we consider a manifold with a dynamical vector field and inquire about the possible tangent bundle structures which would turn the starting vector field into a second order one. The analysis is restricted to manifolds which…

In the framework of metric-like approach, totally symmetric arbitrary spin bosonic conformal fields propagating in flat space-time are studied. Depending on the values of conformal dimension, spin, and dimension of space-time, we classify…

Conformal nets provide a mathematical formalism for conformal field theory. Associated to a conformal net with finite index, we give a construction of the `bundle of conformal blocks', a representation of the mapping class groupoid of…

The classical Liouville Theorem on conformal transformations determines local conformal transformations on the Euclidean space of dimension $\geq 3$. Its natural adaptation to the general framework of Riemannian structures is the 2-rigidity…

For a conformal manifold we introduce the notion of an ambient connection, an affine connection on an ambient manifold of the conformal manifold, possibly with torsion, and with conditions relating it to the conformal structure. The purpose…

We present a number of conditions which are necessary for an n-dimensional projective structure (M,[nabla]) to include the Levi-Civita connection nabla of some metric on M. We provide an algorithm, which effectively checks if a Levi-Civita…

Rational conformal field theories produce a tower of finite-dimensional representations of surface mapping class groups, acting on the conformal blocks of the theory. We review this formalism. We show that many recent mathematical…

We prove that Fefferman spaces, associated to non--degenerate CR structures of hypersurface type, are characterised, up to local conformal isometry, by the existence of a parallel orthogonal complex structure on the standard tractor bundle.…

Conformal blocks form a system of vector bundles over the moduli space of complex curves with marked points. We discuss various aspects of these bundles. In particular, we present conjectures about the dimensions of sub-bundles. They imply…

The study of the packing of a length of wire in a two dimensional domain is done using techniques of conformal maps. The resulting scaling properties are derived through the Coulomb gas formalism of Conformal Field Theories. An analogy is…

The following are expanded lecture notes for the course of eight one hour lectures given by the second author at the 2014 summer school Asymptotic Analysis in General Relativity held in Grenoble by the Institut Fourier. The first four…

We discuss some open problems in a program of constructing and studying two-dimensional conformal field theories using the representation theory of vertex operator algebras.

We construct and fully characterize a scalar boundary conformal field theory on a triangulated Riemann surface. The results are analyzed from a string theory perspective as tools to deal with open/closed string dualities.

A modular tensor category provides the appropriate data for the construction of a three-dimensional topological field theory. We describe the following analogue for two-dimensional conformal field theories: a 2-category whose objects are…

We point out that double categories provide a natural setting for modular functors obtained by a (bicategorical) string-net construction: The source of the modular functor -- which is now a double functor -- is a symmetric monoidal double…

Transports preserving the angle between two contravariant vector fields but changing their lengths proportional to their own lengths are introduced as `conformal' transports and investigated over spaces with one affine connection and…

Conformal field theories have been extremely useful in our quest to understand physical phenomena in many different branches of physics, starting from condensed matter all the way up to high energy. Here we discuss applications of…