A. Mikovic
String Theory and Quantum Spin Networks
Preprint series: ESI preprints

MSC:

81T30 String and superstring theories; other extended objects , See also {83E30}

57R57 Applications of global analysis to structures on manifolds, See also {58-XX}

17B37 Quantum groups and related deformations, See also {16W30, 81R50, 82B23}

17B67 Kac-Moody algebras (structure and representation theory)

PACS: 11.25.Pm,11.25.Hf,0460.Pp
Abstract: We propose an approach to formulating string theory in a curved
spacetime, which is based on the connection between the states of
the WZW model for the isometry group of a background spacetime
metric and the representations of the corresponding quantum group.
In this approach the string states scattering amplitudes are
defined by the evaluations of the theta spin networks for the
associated quantum group. We examine the evaluations given by the
spin network invariants defined by the spin foam state sum model
associated to the two-dimensional BF theory for the background
isometry group. We show that the corresponding string amplitudes
are well-defined if the spacetime manifold is compact and admits a
group metric. We compute the simplest scattering amplitudes in the
case of the SU(2) background isometry group, and we provide
arguments that these are the amplitudes of a topological string
theory.

Keywords: SU(2)-WZW model, BF theory, spin foams