2010/04/07 by Elaine Beltaos, Terry Gannon
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Conformal map #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Minimal model #Minimal models #Modular curve #Modular design #Modular form #Modular invariance #Unitary state #hep-th #math.QA #msc:81T40
paper · pdf · doi:10.1007/s00220-012-1473-4
25 pages
arxiv created 2010/04/07 · openalex publication_date 2012/04/24 · arxiv updated 2015/05/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We first rigourously establish, for any N, that the toroidal modular invariant partition functions for the (not necessarily unitary) WN(p,q) minimal models biject onto a well-defined subset of those of the SU(N)xSU(N) Wess-Zumino-Witten theories at level (p-N,q-N). This permits considerable simplifications to the proof of the Cappelli-Itzykson-Zuber classification of Virasoro minimal models. More important, we obtain from this the complete classification of all modular invariants for the W3(p,q) minimal models. All should be realised by rational conformal field theories. Previously, only those for the unitary models, i.e. W3(p,p+1), were classified. For all N our correspondence yields for free an extensive list of WN(p,q) modular invariants. The W3 modular invariants, like the Virasoro minimal models, all factorise into SU(3) modular invariants, but this fails in general for larger N. We also classify the SU(3)xSU(3) modular invariants, and find there a new infinite series of exceptionals.