Integrating positive energy representations of the Virasoro algebra

TL;DR

This paper demonstrates that unitary positive energy representations of the Virasoro algebra can be extended to holomorphic *-representations of annuli semigroups, linking algebraic and geometric structures in conformal field theory.

Contribution

It establishes a method to exponentiate Virasoro algebra representations to semigroup representations, connecting algebraic and geometric frameworks in conformal nets.

Findings

Unitary positive energy Virasoro representations exponentiate to semigroup representations.

Representations of the Virasoro conformal net extend to annuli semigroups.

Provides a bridge between algebraic and geometric approaches in conformal field theory.

Abstract

We show that every unitary positive energy representation W of the Virasoro algebra exponentiates to a holomorphic *-representation of the semigroup of annuli by bounded operators on the Hilbert space completion of W. We use this to show that every representation of the Virasoro conformal net also carries a representation of the semigroup of annuli of the same kind.