Karl-Georg Schlesinger
A Universal Symmetry Structure in Open String Theory
Preprint series: ESI preprints

MSC:

81T16 Nonperturbative methods of renormalization

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

PACS: 02.10.De,11.25.Sq
Abstract: In this paper, we arrive from different starting points at the conclusion
that the symmetry given by an action of the Grothendieck-Teichm\"{u}ller
group $GT$ on the so called extended moduli space of string theory can not
be physical - in the sense that it does not survive the inclusion of general
nonperturbative vacua given by boundary condition on the level of two
dimensional conformal field theory - but has to be extended to a quantum
symmetry given by a self-dual, noncommutative, and noncocommutative Hopf
algebra $\mathcal{H}_{GT}$. First, we show that a class of two dimensional
boundary conformal field theories always uniquely defines a trialgebra and
find $\mathcal{H}_{GT}$ as the universal symmetry of such trialgebras (in
analogy to the definition of $GT$ as the universal symmetry of
quasi-triangular quasi-Hopf algebras). Second, we argue in a more heuristic
approach that the $\mathcal{H}_{GT}$ symmetry can also be found in a more
geometric picture using the language of gerbes. Finally, we will see that
the fact that the $GT$ symmetry can not be physical in the above sense can
also be seen by trying to understand why the action of $GT$ on the
Duflo-Kirillov isomorphism which is considered in \cite{Kon 1999}
trivializes.

Keywords: string theory, deformation quantization, motives