Conformal Field Theory and Torsion Elements of the Bloch Group

Werner Nahm ()

A chapter in Frontiers in Number Theory, Physics, and Geometry II, 2007, pp 67-132 from Springer

Abstract: Abstract We argue that rational conformally invariant quantum field theories in two dimensions are closely related to torsion elements of the algebraic K-theory group K3(C). If such a field theory has an integrable perturbation with purely elastic scattering matrix, then its partition function has a canonical sum representation. The corresponding asymptotic behaviour of the density of states is given in terms of the solutions of an algebraic equation which can be read off from the scattering matrix. These solutions yield torsion elements of an extension of the Bloch group which seems to be equal to K3(C). The algebraic equations are solved for integrable models given by arbitrary pairs of A-type Cartan matrices. The paper should be readable by mathematicians.

Keywords: Central Charge; Irreducible Representation; Operator Product Expansion; Conformal Dimension; Dynkin Diagram (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-30308-4_2

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DOI: 10.1007/978-3-540-30308-4_2

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