7,558 research outputs found
Convolution of convex valuations
We show that the natural "convolution" on the space of smooth, even,
translation-invariant convex valuations on a euclidean space , obtained by
intertwining the product and the duality transform of S. Alesker, may be
expressed in terms of Minkowski sum. Furthermore the resulting product extends
naturally to odd valuations as well. Based on this technical result we give an
application to integral geometry, generalizing Hadwiger's additive kinematic
formula for to general compact groups acting
transitively on the sphere: it turns out that these formulas are in a natural
sense dual to the usual (intersection) kinematic formulas.Comment: 18 pages; Thm. 1.4. added; references updated; other minor changes;
to appear in Geom. Dedicat
Holographic fractional topological insulators in 2+1 and 1+1 dimensions
We give field theory descriptions of the time-reversal invariant quantum spin
Hall insulator in 2+1 dimensions and the particle-hole symmetric insulator in
1+1 dimensions in terms of massive Dirac fermions. Integrating out the massive
fermions we obtain a low-energy description in terms of a topological field
theory, which is entirely determined by anomaly considerations. This
description allows us to easily construct low-energy effective actions for the
corresponding `fractional' topological insulators, potentially corresponding to
new states of matter. We give a holographic realization of these fractional
states in terms of a probe brane system, verifying that the expected
topologically protected transport properties are robust even at strong
coupling.Comment: 13 pages, 1 figure, version accepted for publication in Phys. Rev.
Introduction to \u3cem\u3eGuiding Global Order: G8 Governance in the Twenty First Century\u3c/em\u3e
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