Conformal theory of curves with tractors

The Conformal Theory of Curves.

Quantum curves and conformal field theory

To a given algebraic curve we assign an infinite family of quantum curves (Schrödinger equations), which are in one-to-one correspondence with, and have the structure of, Virasoro singular vectors. For a spectral curve of a matrix model we build such quantum curves out of an appropriate representation of the Virasoro algebra, encoded in the structure of the α/β-deformed matrix integral and its ...

Standard Tractors and the Conformal Ambient Metric Construction

In this paper we relate the Fefferman–Graham ambient metric construction for conformal manifolds to the approach to conformal geometry via the canonical Cartan connection. We show that from any ambient metric that satisfies a weakening of the usual normalisation condition, one can construct the conformal standard tractor bundle and the normal standard tractor connection, which are equivalent to...

Conformal field theory and integrable systems associated to elliptic curves

It has become clear over the years that quantum groups (i.e., quasitriangular Hopf algebras, see [D]) and their semiclassical counterpart, Poisson Lie groups, are an essential algebraic structure underlying three related subjects: integrable models of statistical mechanics, conformal field theory and integrable models of quantum field theory in 1+1 dimensions. Still, some points remain obscure ...

Conformal Images of Carleson Curves

We show that if γ is a curve in the unit disk, then arclength on γ is a Carleson measure iff the image of γ has finite length under every conformal map onto a domain with rectifiable boundary. Date: July 27, 2012. 1991 Mathematics Subject Classification. Primary: 30C62 Secondary: