835 research outputs found
On the Killing form of Lie Algebras in Symmetric Ribbon Categories
As a step towards the structure theory of Lie algebras in symmetric monoidal
categories we establish results involving the Killing form. The proper
categorical setting for discussing these issues are symmetric ribbon
categories
A note on permutation twist defects in topological bilayer phases
We present a mathematical derivation of some of the most important physical
quantities arising in topological bilayer systems with permutation twist
defects as introduced by Barkeshli et al. in cond-mat/1208.4834. A crucial tool
is the theory of permutation equivariant modular functors developed by Barmeier
et al. in math.CT/0812.0986 and math.QA/1004.1825.Comment: 18 pages, some figure
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
TFT construction of RCFT correlators IV: Structure constants and correlation functions
We compute the fundamental correlation functions in two-dimensional rational
conformal field theory, from which all other correlators can be obtained by
sewing: the correlators of three bulk fields on the sphere, one bulk and one
boundary field on the disk, three boundary fields on the disk, and one bulk
field on the cross cap. We also consider conformal defects and calculate the
correlators of three defect fields on the sphere and of one defect field on the
cross cap.
Each of these correlators is presented as the product of a structure constant
and the appropriate conformal two- or three-point block. The structure
constants are expressed as invariants of ribbon graphs in three-manifolds.Comment: 98 pages, some figures; v2 (version published in NPB): typos
correcte
Universal simple current vertex operators
We construct a vertex operator realization for the simple current primary
fields of WZW theories which are based on simply laced affine Lie algebras g.
This is achieved by employing an embedding of the integrable highest weight
modules of g into the Fock space for a bosonic string compactified on the
weight lattice of g. Our vertex operators are universal in the sense that a
single expression for the vertex operator holds simultaneously for all positive
integral values of the level of g.Comment: 17 pages, LaTeX2
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