14,635 research outputs found
Branching rules of semi-simple Lie algebras using affine extensions
We present a closed formula for the branching coefficients of an embedding p
in g of two finite-dimensional semi-simple Lie algebras. The formula is based
on the untwisted affine extension of p. It leads to an alternative proof of a
simple algorithm for the computation of branching rules which is an analog of
the Racah-Speiser algorithm for tensor products. We present some simple
applications and describe how integral representations for branching
coefficients can be obtained. In the last part we comment on the relation of
our approach to the theory of NIM-reps of the fusion rings of WZW models with
chiral algebra g_k. In fact, it turns out that for these models each embedding
p in g induces a NIM-rep at level k to infinity. In cases where these NIM-reps
can be be extended to finite level, we obtain a Verlinde-like formula for
branching coefficients.Comment: 11 pages, LaTeX, v2: one reference added, v3: Clarified proof of
Theorem 2, completely rewrote and extended Section 5 (relation to CFT), added
various references. Accepted for publication in J. Phys.
Commutative Algebras in Fibonacci Categories
By studying NIM-representations we show that the Fibonacci category and its
tensor powers are completely anisotropic; that is, they do not have any
non-trivial separable commutative ribbon algebras. As an application we deduce
that a chiral algebra with the representation category equivalent to a product
of Fibonacci categories is maximal; that is, it is not a proper subalgebra of
another chiral algebra. In particular the chiral algebras of the Yang-Lee
model, the WZW models of G2 and F4 at level 1, as well as their tensor powers,
are maximal
KP-approach for non-symmetric short-range defects: resonant states and alloy bandstructure
The short-range defect with reduced symmetry is studied in the framework of
KP-approach taking into account a matrix structure of potential energy in the
equations for envelope functions. The case of the narrow-gap semiconductor,
with defects which are non-symmetric along the [001], [110], or [111]
directions, is considered. Resonant state at a single defect is analyzed within
the Koster-Slater approximation. The bandstructure modification of the alloy,
formed by non-symmetric impurities, is discussed and a generalized virtual
crystal approximation is introduced.Comment: Extended version, 9 pages, 6 figures (EPS
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
Boundary states for WZW models
The boundary states for a certain class of WZW models are determined. The
models include all modular invariants that are associated to a symmetry of the
unextended Dynkin diagram. Explicit formulae for the boundary state
coefficients are given in each case, and a number of properties of the
corresponding NIM-reps are derived.Comment: 34 pages, harvmac (b), 4 eps-figures. One reference added; some minor
typos, as well as the embedding into , are correcte
The charges of a twisted brane
The charges of the twisted D-branes of certain WZW models are determined. The
twisted D-branes are labelled by twisted representations of the affine algebra,
and their charge is simply the ground state multiplicity of the twisted
representation. It is shown that the resulting charge group is isomorphic to
the charge group of the untwisted branes, as had been anticipated from a
K-theory calculation. Our arguments rely on a number of non-trivial Lie
theoretic identities.Comment: 27 pages, 1 figure, harvmac (b
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