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Conformal Field Theory and Torsion Elements of the Bloch Group

In: Frontiers in Number Theory, Physics, and Geometry II

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  • Werner Nahm

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.

Suggested Citation

  • Werner Nahm, 2007. "Conformal Field Theory and Torsion Elements of the Bloch Group," Springer Books, in: Pierre Cartier & Pierre Moussa & Bernard Julia & Pierre Vanhove (ed.), Frontiers in Number Theory, Physics, and Geometry II, pages 67-132, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-30308-4_2
    DOI: 10.1007/978-3-540-30308-4_2
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