Virasoro Representations on (Diff S1)/S1 Coadjoint Orbits

TL;DR

This paper constructs new Virasoro algebra representations on a bosonic Fock space via coadjoint orbits of (Diff S1)/S1, analyzing their structure, characters, and reducibility, thus advancing understanding of their unitary properties.

Contribution

It introduces explicit realizations of Virasoro representations on Fock space associated with (Diff S1)/S1 coadjoint orbits and investigates their unitarity and reducibility.

Findings

Characters match Witten's bosonic partition functions.

Representations for c <= 1 are reducible, confirming a prior conjecture.

Progress in understanding the unitary structure of these representations.

Abstract

A new set of realizations of the Virasoro algebra on a bosonic Fock space are found by explicitly computing the Virasoro representations associated with coadjoint orbits of the form (Diff S1) / S1. Some progress is made in understanding the unitary structure of these representations. The characters of these representations are exactly the bosonic partition functions calculated previously by Witten using perturbative and fixed-point methods. The representations corresponding to the discrete series of unitary Virasoro representations with c <= 1 are found to be reducible in this formulation, confirming a conjecture by Aldaya and Navarro-Salas.