2,638 research outputs found
Anyons in Geometric Models of Matter
We show that the "geometric models of matter" approach proposed by the first
author can be used to construct models of anyon quasiparticles with fractional
quantum numbers, using 4-dimensional edge-cone orbifold geometries with
orbifold singularities along embedded 2-dimensional surfaces. The anyon states
arise through the braid representation of surface braids wrapped around the
orbifold singularities, coming from multisections of the orbifold normal bundle
of the embedded surface. We show that the resulting braid representations can
give rise to a universal quantum computer.Comment: 22 pages LaTe
Matrix Factorizations, Minimal Models and Massey Products
We present a method to compute the full non-linear deformations of matrix
factorizations for ADE minimal models. This method is based on the calculation
of higher products in the cohomology, called Massey products. The algorithm
yields a polynomial ring whose vanishing relations encode the obstructions of
the deformations of the D-branes characterized by these matrix factorizations.
This coincides with the critical locus of the effective superpotential which
can be computed by integrating these relations. Our results for the effective
superpotential are in agreement with those obtained from solving the A-infinity
relations. We point out a relation to the superpotentials of Kazama-Suzuki
models. We will illustrate our findings by various examples, putting emphasis
on the E_6 minimal model.Comment: 32 pages, v2: typos corrected, v3: additional comments concerning the
bulk-boundary crossing constraint, some small clarifications, typo
Partial holomorphic connections and extension of foliations
This paper stresses the strong link between the existence of partial
holomorphic connections on the normal bundle of a foliation seen as a quotient
of the ambient tangent bundle and the extendability of a foliation to an
infinitesimal neighborhood of a submanifold. We find the obstructions to
extendability and thanks to the theory developed we obtain some new
Khanedani-Lehmann-Suwa type index theorems
Subfactors of index less than 5, part 2: triple points
We summarize the known obstructions to subfactors with principal graphs which
begin with a triple point. One is based on Jones's quadratic tangles
techniques, although we apply it in a novel way. The other two are based on
connections techniques; one due to Ocneanu, and the other previously
unpublished, although likely known to Haagerup.
We then apply these obstructions to the classification of subfactors with
index below 5. In particular, we eliminate three of the five families of
possible principal graphs called "weeds" in the classification from
arXiv:1007.1730.Comment: 28 pages, many figures. Completely revised from v1: many additional
or stronger result
Remarks on non-commutative crepant resolutions of complete intersections
We study obstructions to existence of non-commutative crepant resolutions, in
the sense of Van den Bergh, over local complete intersections
Highly connected manifolds with positive Ricci curvature
We prove the existence of Sasakian metrics with positive Ricci curvature on
certain highly connected odd dimensional manifolds. In particular, we show that
manifolds homeomorphic to the 2k-fold connected sum of S^{2n-1} x S^{2n} admit
Sasakian metrics with positive Ricci curvature for all k. Furthermore, a
formula for computing the diffeomorphism types is given and tables are
presented for dimensions 7 and 11.Comment: This is the version published by Geometry & Topology on 29 November
200
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