Ground state representations of some non-rational conformal nets

TL;DR

This paper constructs new ground state representations for certain conformal nets, revealing their non-covariance properties and introducing potential new M"obius covariant nets on the circle.

Contribution

It introduces families of ground state representations for U(1)-current and Virasoro nets, highlighting their non-covariance and potential for new covariant nets.

Findings

Ground state representations are not covariant under original dilations.

U(1)-current net representations are not solitonic.

Dual nets may yield new M"obius covariant nets.

Abstract

We construct families of ground state representations of the U(1)-current net and of the Virasoro nets Vir_c with central charge c >= 1. We show that these representations are not covariant with respect to the original dilations, and those on the U(1)-current net are not solitonic. Furthermore, by going to the dual net with respect to the ground state representations of Vir_c, we obtain a possibly new family of M\"obius covariant nets on S^1.