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arxiv: hep-th/0203183 · v2 · submitted 2002-03-20 · ✦ hep-th

A universal symmetry structure in open string theory

classification ✦ hep-th
keywords symmetryalgebragivenhopftheoryuniversalboundaryconformal
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In this paper, we arrive from different starting points at the conclusion that the symmetry given by an action of the Grothendieck-Teichmueller 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 conditions 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. First, we show that a class of two dimensional boundary conformal field theories always uniquely defines a trialgebra and find the above mentioned Hopf algebra 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 this Hopf algebra symmetry can also be found in a more geometric picture using the language of gerbes.

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