23 research outputs found
Topological and conformal field theory as Frobenius algebras
Two-dimensional conformal field theory (CFT) can be defined through its
correlation functions. These must satisfy certain consistency conditions which
arise from the cutting of world sheets along circles or intervals. The
construction of a (rational) CFT can be divided into two steps, of which one is
complex-analytic and one purely algebraic. We realise the algebraic part of the
construction with the help of three-dimensional topological field theory and
show that any symmetric special Frobenius algebra in the appropriate braided
monoidal category gives rise to a solution. A special class of examples is
provided by two-dimensional topological field theories, for which the relevant
monoidal category is the category of vector spaces.Comment: 23 pages, several figures, proceedings to the Streetfest (Canberra
07/2005); v2: section 2.4 expanded, version accepted for publication in
Contemp. Mat
Partition functions, mapping class groups and Drinfeld doubles
Higher genus partition functions of two-dimensional conformal field theories
have to be invariants under linear actions of mapping class groups. We
illustrate recent results [4,6] on the construction of such invariants by
concrete expressions obtained for the case of Drinfeld doubles of finite
groups. The results for doubles are independent of the characteristic of the
underlying field, and the general results do not require any assumptions of
semisimplicity.Comment: Slightly extended version of contribution to the Proceedings of the
XXIX International Colloquium on Group-Theoretical Methods in Physics
(Tianjin, August 2012). v2: typos correcte
A no-ghost theorem for the bosonic Nappi-Witten string
We prove a no-ghost theorem for a bosonic string propagating in Nappi-Witten
spacetime. This is achieved in two steps. We first demonstrate unitarity for a
class of NW/U(1) modules: the norm of any state which is primary with respect
to a chosen timelike U(1) is non-negative. We then show that physical states -
states satisfying the Virasoro constraints - in a class of modules of an
affinisation of the Nappi-Witten algebra are contained in the NW/U(1) modules.
Similar to the case of strings on , in order to saturate the spectrum
obtained in light-cone quantization we are led to include modules with energy
not bounded from below, which are related to modules with energy bounded from
below by spectral flow automorphisms.Comment: 24 pages, 1 figur
CFT description of three-dimensional Kerr-de Sitter spacetime
We describe three-dimensional Kerr-de Sitter space using similar methods as
recently applied to the BTZ black hole. A rigorous form of the classical
connection between gravity in three dimensions and two-dimensional conformal
field theory is employed, where the fundamental degrees of freedom are
described in terms of two dependent SL(2,C) currents. In contrast to the BTZ
case, however, quantization does not give the Bekenstein-Hawking entropy
connected to the cosmological horizon of Kerr-de Sitter space.Comment: 12 pages, v2: references added and some structural change