D-Brane Conformal Field Theory and Bundles of Conformal Blocks

Schweigert, Christoph; Fuchs, Jürgen

doi:10.1007/978-3-0348-8266-8_42

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The Strategy For Obtaining the Boundary Classifying Algebra ...1

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2011

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“…with complex numbers C qγ ıα,kβ that do not depend on the elementary boundary condition M. The latter numbers, which are obtained as traces on spaces of conformal blocks [37], can be used to define an associative multiplication on the space B A := ı∈I Hom A|A (U ı ⊗ + A ⊗ − U ī, A) of left-right symmetric bulk fields, i.e. they play the role of the structure constants of the algebra B A .…”

Section: The Strategy For Obtaining the Boundary Classifying Algebra ...mentioning

confidence: 99%

The classifying algebra for defects

Fuchs¹,

Schweigert²,

Stigner³

2011

Nuclear Physics B

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We demonstrate that topological defects in a rational conformal field theory can be described by a classifying algebra for defects -a finite-dimensional semisimple unital commutative associative algebra whose irreducible representations give the defect transmission coefficients. We show in particular that the structure constants of the classifying algebra are traces of operators on spaces of conformal blocks and that the defect transmission coefficients determine the defect partition functions.

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Section: The Strategy For Obtaining the Boundary Classifying Algebra ...mentioning

confidence: 99%