186 research outputs found
Galois Modular Invariants of WZW Models
The set of modular invariants that can be obtained from Galois
transformations is investigated systematically for WZW models. It is shown that
a large subset of Galois modular invariants coincides with simple current
invariants. For algebras of type B and D infinite series of previously unknown
exceptional automorphism invariants are found.Comment: phyzzx macros, 38 pages. NIKHEF-H/94-3
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
Quasi-Galois Symmetries of the Modular S-Matrix
The recently introduced Galois symmetries of RCFT are generalized, for the
WZW case, to `quasi-Galois symmetries'. These symmetries can be used to derive
a large number of equalities and sum rules for entries of the modular matrix S,
including some that previously had been observed empirically. In addition,
quasi-Galois symmetries allow to construct modular invariants and to relate
S-matrices as well as modular invariants at different levels. They also lead us
to an extremely plausible conjecture for the branching rules of the conformal
embeddings of g into so(dim g).Comment: 20 pages (A4), LaTe
Comments on nonunitary conformal field theories
As is well-known, nonunitary RCFTs are distinguished from unitary ones in a
number of ways, two of which are that the vacuum 0 doesn't have minimal
conformal weight, and that the vacuum column of the modular S matrix isn't
positive. However there is another primary field, call it o, which has minimal
weight and has positive S column. We find that often there is a precise and
useful relationship, which we call the Galois shuffle, between primary o and
the vacuum; among other things this can explain why (like the vacuum) its
multiplicity in the full RCFT should be 1. As examples we consider the minimal
WSU(N) models. We conclude with some comments on fractional level admissible
representations of affine algebras. As an immediate consequence of our
analysis, we get the classification of an infinite family of nonunitary WSU(3)
minimal models in the bulk.Comment: 24 page
Automorphism Modular Invariants of Current Algebras
We consider those two-dimensional rational conformal field theories (RCFTs)
whose chiral algebras, when maximally extended, are isomorphic to the current
algebra formed from some affine non-twisted Kac--Moody algebra at fixed level.
In this case the partition function is specified by an automorphism of the
fusion ring and corresponding symmetry of the Kac--Peterson modular matrices.
We classify all such partition functions when the underlying finite-dimensional
Lie algebra is simple. This gives all possible spectra for this class of RCFTs.
While accomplishing this, we also find the primary fields with second smallest
quantum dimension.Comment: 32 pages, plain Te
A classifying algebra for boundary conditions
We introduce a finite-dimensional algebra that controls the possible boundary
conditions of a conformal field theory. For theories that are obtained by
modding out a Z_2 symmetry (corresponding to a so-called D_odd-type, or
half-integer spin simple current, modular invariant), this classifying algebra
contains the fusion algebra of the untwisted sector as a subalgebra. Proper
treatment of fields in the twisted sector, so-called fixed points, leads to
structures that are intriguingly close to the ones implied by modular
invariance for conformal field theories on closed orientable surfaces.Comment: 12 pages, LaTe
Finite Group Modular Data
In a remarkable variety of contexts appears the modular data associated to
finite groups. And yet, compared to the well-understood affine algebra modular
data, the general properties of this finite group modular data has been poorly
explored. In this paper we undergo such a study. We identify some senses in
which the finite group data is similar to, and different from, the affine data.
We also consider the data arising from a cohomological twist, and write down,
explicitly in terms of quantities associated directly with the finite group,
the modular S and T matrices for a general twist, for what appears to be the
first time in print.Comment: 38 pp, latex; 5 references added, "questions" section touched-u
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