1992/11/13 by Werner Nahm, W. Nahm, A. Recknagel +2 · 3 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Central charge #Conformal field theory #Conformal map #Conformal symmetry #Field (mathematics) #Fusion #Fusion rules #Geometry #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematical proof #Mathematics #Philosophy #Physics #Pure mathematics #Quantum field theory #Theoretical physics #hep-th
paper · pdf · doi:10.1142/s0217732393001562
published as Mod.Phys.Lett. A8 (1993) 1835-1848 · 14 pages, BONN-preprint. (a few minor changes, two major corrections in chapter 3, namely: (3.10) only holds in the case of the A series, Goncharovs conjecture is not an equivalence but rather an implication and a theorem)
arxiv created 1992/11/13 · openalex publication_date 1993/06/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Dilogarithm identities for the central charges and conformal dimensions exist for at least large classes of rational conformally invariant quantum field theories in two dimensions. In many cases, proofs are not yet known but the numerical and structural evidence is convincing. In particular, close relations exist to fusion rules and partition identities. We describe some examples and ideas, and present conjectures useful for the classification of conformal theories. The mathematical structures seem to be dual to Thurston’s program for the classification of three-manifolds.