Ground State Representations of Some Non-Rational Conformal 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 , one obtains possibly new family of Möbius covariant nets on S 1 .