The three-dimensional origin of the classifying algebra

被引：4

作者：

Fuchs, Juergen ^{[1
]}

Schweigert, Christoph ^{[2
]}

Stigner, Carl ^{[1
]}

机构：

[1] Karlstad Univ, S-65188 Karlstad, Germany

[2] Univ Hamburg, Bereich Algebra & Zuhlentheorie, D-20146 Hamburg, Germany

来源：

NUCLEAR PHYSICS B | 2010年 / 824卷 / 03期

关键词：

Conformal field theory; Factorization; Boundary conditions; Classifying algebra; Conformal blocks; BOUNDARY OPERATORS; TFT CONSTRUCTION; SYMMETRY; BULK;

D O I：

10.1016/j.nuclphysb.2009.07.017

中图分类号：

O412 [相对论、场论]; O572.2 [粒子物理学];

学科分类号：

摘要：

It is known that reflection coefficients for bulk fields of a rational conformal field theory in the presence of an elementary boundary condition can be obtained as representation matrices of irreducible representations of the classifying algebra, a semisimple commutative associative complex algebra. We show how this algebra arises naturally from the three-dimensional geometry of factorization of correlators of bulk fields on the disk. This allows us to derive explicit expressions for the structure constants of the classifying algebra as invariants of ribbon graphs in the three-manifold S-2 x S-1. Our result unravels a precise relation between intertwiners of the action of the mapping class group on spaces of conformal blocks and boundary conditions in rational conformal field theories. (c) 2009 Elsevier B.V. All rights reserved.

引用

页码：333 / 364

页数：32

共 40 条

[1] UNIVERSAL NONINTEGER GROUND-STATE DEGENERACY IN CRITICAL QUANTUM-SYSTEMS [J].