A weight two vector v of a vertex operator algebra is called a conformal vector with central charge c if the component operators Lv(n) for n ∈ Z of Y (v, z) = ∑ n∈Z Lv(n)z −n−2 satisfy the Virasoro algebra relation with central charge c. In this case, the vertex operator subalgebra Vir(v) generated by v is isomorphic to a Virasoro vertex operator algebra with central charge c ([FZ], [M]). Let V...

We describe how a natural lattice analogue of the abelian current algebra combined with free discrete time dynamics gives rise to the lattice Virasoro algebra and corresponding hierarchy of conservation laws.

The coadjoint orbits of the Virasoro group, which have been investigated by Lazutkin and Pankratova and by Segal, should according to the Kirillov-Kostant theory be related to the unitary representations of the Virasoro group. In this paper, the classification of orbits is reconsidered, with an explicit description of the possible centralizers of coadjoint orbits. The possible orbits are diff(S...

The number of ghost states at each energy level in a non-unitary con-formal field theory is encoded in the signature characters of the relevant Virasoro algebra highest weight representations. We give expressions for these signature characters. These results complete Friedan-Qiu-Shenker's analysis of the Virasoro algebra's highest weight representations.

2 Vertex Operator Algebras 6 2.1 Notation and Conventions . . . . . . . . . . . . . . . . . . . . 6 2.2 Local Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Axioms for a Vertex Algebra . . . . . . . . . . . . . . . . . . . 9 2.4 Heisenberg Algebra . . . . . . . . . . . . . . . . . . . . . . . . 11 2.5 Virasoro Algebra . . . . . . . . . . . . . . . . . . . . . . . . . 13 2....

A bstract Conformal Carroll symmetry generically arises on null manifolds and is important for holography of asymptotically flat spacetimes, generic black hole horizons tensionless strings. In this paper, we focus two dimensional (2 d ) hence the 2 or equivalently 3 Bondi-Metzner-Sachs (BMS) algebra. Using covariance, write most general free massless scalar field theory discover three inequival...