149 research outputs found
Higher level twisted Zhu algebras
The study of twisted representations of graded vertex algebras is important
for understanding orbifold models in conformal field theory. In this paper we
consider the general set-up of a vertex algebra , graded by \G/\Z for some
subgroup \G of containing , and with a Hamiltonian operator
having real (but not necessarily integer) eigenvalues. We construct the
directed system of twisted level Zhu algebras \zhu_{p, \G}(V), and we
prove the following theorems: For each there is a bijection between the
irreducible \zhu_{p, \G}(V)-modules and the irreducible \G-twisted positive
energy -modules, and is (\G, H)-rational if and only if all its Zhu
algebras \zhu_{p, \G}(V) are finite dimensional and semisimple. The main
novelty is the removal of the assumption of integer eigenvalues for . We
provide an explicit description of the level Zhu algebras of a universal
enveloping vertex algebra, in particular of the Virasoro vertex algebra
\vir^c and the universal affine Kac-Moody vertex algebra V^k(\g) at
non-critical level. We also compute the inverse limits of these directed
systems of algebras.Comment: 47 pages, no figure
A quantum field comonad
We encapsulate the basic notions of the theory of vertex algebras into the
construction of a comonad on an appropriate category of formal distributions.
Vertex algebras are recovered as coalgebras over this comonad.Comment: 13 page
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