12,902 research outputs found
Coset Realization of Unifying W-Algebras
We construct several quantum coset W-algebras, e.g. sl(2,R)/U(1) and
sl(2,R)+sl(2,R) / sl(2,R), and argue that they are finitely nonfreely
generated. Furthermore, we discuss in detail their role as unifying W-algebras
of Casimir W-algebras. We show that it is possible to give coset realizations
of various types of unifying W-algebras, e.g. the diagonal cosets based on the
symplectic Lie algebras sp(2n) realize the unifying W-algebras which have
previously been introduced as `WD_{-n}'. In addition, minimal models of WD_{-n}
are studied. The coset realizations provide a generalization of
level-rank-duality of dual coset pairs. As further examples of finitely
nonfreely generated quantum W-algebras we discuss orbifolding of W-algebras
which on the quantum level has different properties than in the classical case.
We demonstrate in some examples that the classical limit according to Bowcock
and Watts of these nonfreely finitely generated quantum W-algebras probably
yields infinitely nonfreely generated classical W-algebras.Comment: 60 pages (plain TeX) (final version to appear in Int. J. Mod. Phys.
A; several minor improvements and corrections - for details see beginning of
file
Orbifolds of Lattice Vertex Operator Algebras at and
Motivated by the notion of extremal vertex operator algebras, we investigate
cyclic orbifolds of vertex operator algebras coming from extremal even
self-dual lattices in and . In this way we construct about one
hundred new examples of holomorphic VOAs with a small number of low weight
states.Comment: 18 pages, LaTe
Cyclic cohomology for graded -algebras and its pairings with van Daele -theory
We consider cycles for graded -algebras (Real -algebras)
which are compatible with the -structure and the real structure. Their
characters are cyclic cocycles. We define a Connes type pairing between such
characters and elements of the van Daele -groups of the -algebra
and its real subalgebra. This pairing vanishes on elements of finite order. We
define a second type of pairing between characters and -group elements which
is derived from a unital inclusion of -algebras. It is potentially
non-trivial on elements of order two and torsion valued. Such torsion valued
pairings yield topological invariants for insulators. The two-dimensional
Kane-Mele and the three-dimensional Fu-Kane-Mele strong invariant are special
cases of torsion valued pairings. We compute the pairings for a simple class of
periodic models and establish structural results for two dimensional aperiodic
models with odd time reversal invariance.Comment: 57 page
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