Conformal Field Theory and Torsion Elements of the Bloch Group
Abstract
We argue that rational conformally invariant quantum field theories in two dimensions are closely related to torsion elements of the algebraic Ktheory group K_3(C). If such a theory has an integrable matrix perturbation with purely elastic scattering matrix, then the partition function has a canonical sum representation. Its asymptotic behaviour is given in terms of the solution of an algebraic equation which can be read off from the scattering matrix. The solutions yield torsion elements of an extension of the Bloch group which seems to be equal to K_3(C). These algebraic equations are solved for integrable models given by arbitrary pairs of equations are solved for integrable models given by arbitrary pairs of Atype Cartan matrices. The paper should be readable by mathematicians.
 Publication:

arXiv eprints
 Pub Date:
 April 2004
 arXiv:
 arXiv:hepth/0404120
 Bibcode:
 2004hep.th....4120N
 Keywords:

 High Energy Physics  Theory;
 Number Theory;
 KTheory and Homology
 EPrint:
 Contribution to Les Houches Lecture Notes, March 2003, 63 pages