Communications in Mathematical Physics

, Volume 174, Issue 3, pp 605–633 | Cite as

Characterizing invariants for local extensions of current algebras

  • Karl-Henning Rehren
  • Yassen S. Stanev
  • Ivan T. Todorov


ParisA ⊂ ℬ of local quantum field theories are studied, whereA is a chiral conformal quantum field theory and ℬ is a local extension, either chiral or two-dimensional. The local correlation functions of fields from ℬ have an expansion with respect toA into conformal blocks, which are non-local in general. Two methods of computing characteristic invariant ratios of structure constants in these expansions are compared: (a) by constructing the monodromy representation of the braid group in the space of solutions of the Knizhnik-Zamolodchikov differential equation, and (b) by an analysis of the local subfactors associated with the extension with methods from operator algebra (Jones theory) and algebraic quantum field theory. Both approaches apply also to the reverse problem: the characterization and (in principle) classification of local extensions of a given theory.


Correlation Function Quantum Field Theory Structure Constant Operator Algebra Conformal Block 
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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Karl-Henning Rehren
    • 1
  • Yassen S. Stanev
    • 2
    • 3
  • Ivan T. Todorov
    • 2
    • 3
  1. 1.II. Institut für Theoretische PhysikUniversität HamburgHamburgGermany
  2. 2.Erwin Schrödinger International Institute for Mathematical PhysicsWienAustria
  3. 3.Institute for Nuclear Research and Nuclear EnergyBulgarian Academy of SciencesSofiaBulgaria

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