2,075 research outputs found
The W_N minimal model classification
We first rigourously establish, for any N, that the toroidal modular
invariant partition functions for the (not necessarily unitary) W_N(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 W_3(p,q) minimal models. All
should be realised by rational conformal field theories. Previously, only those
for the unitary models, i.e. W_3(p,p+1), were classified. For all N our
correspondence yields for free an extensive list of W_N(p,q) modular
invariants. The W_3 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.Comment: 25 page
On Fusion Algebras and Modular Matrices
We consider the fusion algebras arising in e.g. Wess-Zumino-Witten conformal
field theories, affine Kac-Moody algebras at positive integer level, and
quantum groups at roots of unity. Using properties of the modular matrix ,
we find small sets of primary fields (equivalently, sets of highest weights)
which can be identified with the variables of a polynomial realization of the
fusion algebra at level . We prove that for many choices of rank
and level , the number of these variables is the minimum possible, and we
conjecture that it is in fact minimal for most and . We also find new,
systematic sources of zeros in the modular matrix . In addition, we obtain a
formula relating the entries of at fixed points, to entries of at
smaller ranks and levels. Finally, we identify the number fields generated over
the rationals by the entries of , and by the fusion (Verlinde) eigenvalues.Comment: 28 pages, plain Te
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