20,751 research outputs found
Gapless edges of 2d topological orders and enriched monoidal categories
In this work, we give a precise mathematical description of a fully chiral
gapless edge of a 2d topological order (without symmetry). We show that the
observables on the 1+1D world sheet of such an edge consist of a family of
topological edge excitations, boundary CFT's and walls between boundary CFT's.
These observables can be described by a chiral algebra and an enriched monoidal
category. This mathematical description automatically includes that of gapped
edges as special cases. Therefore, it gives a unified framework to study both
gapped and gapless edges. Moreover, the boundary-bulk duality also holds for
gapless edges. More precisely, the unitary modular tensor category that
describes the 2d bulk phase is exactly the Drinfeld center of the enriched
monoidal category that describes the gapless/gapped edge. We propose a
classification of all gapped and fully chiral gapless edges of a given bulk
phase. In the end, we explain how modular-invariant bulk conformal field
theories naturally emerge on certain gapless walls between two trivial phases.Comment: 26 pages, 8 figures, An explanation of the appearance of boundary
CFT's on a chiral gapless edge, which is based on a generalized "no-go
theorem", is added. Final versio
A trace formula for the forcing relation of braids
The forcing relation of braids has been introduced for a 2-dimensional
analogue of the Sharkovskii order on periods for maps of the interval. In this
paper, by making use of the Nielsen fixed point theory and a representation of
braid groups, we deduce a trace formula for the computation of the forcing
order.Comment: 24 pages, 9 figure
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