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.

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.

Convolution of convex valuations

We show that the natural "convolution" on the space of smooth, even, translation-invariant convex valuations on a euclidean space $V$, 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 $SO(V)$ to general compact groups $G \subset O(V)$ 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

How you export matters: the disassortative structure of international trade

The local network structure of international trade relations offers a new dimension for understanding a country’s competitive position vis-á-vis its trade partners and competitors, supporting economic policy analysis. We introduce two network measures that can be used to analyse comparative advantage and price competitiveness, called relative export density and export price assortativity, respectively. The novelty of these measures is that they consider the embedding of a country into its local trade environment. They are computed based on unit values and sector concentrations at a highly granular level and they help to uncover general patterns of the global organisation of international trade. Countries have a strong tendency to arrange their exports to form local monopolies by focusing on products and markets, usually - but not exclusively - where they have a price advantage. Price (dis)assortativity turns out to be an important factor for export growth, even after controlling for a large set of macroeconomic and structural determinants. This effect is particularly strong for catching-up CESEE countries, with potential implications for industrial policy. The relationship between the two export assortativity metrics for different groups of countries and for varying technological content of exports indicates a tipping point in a country’s development from price-driven competition to non-price factors

Convolution of convex valuations

We show that the natural "convolution” on the space of smooth, even, translation-invariant convex valuations on a euclidean space V, obtained by intertwining the product and the duality transform of S. Alesker J. Differential Geom. 63: 63-95, 2003; Geom.Funct. Anal. 14:1-26, 2004 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 SO(V) Convex Geometry, North Holland, 1993 to general compact groups $$G \subset O(V)$$ acting transitively on the sphere: it turns out that these formulas are in a natural sense dual to the usual (intersection) kinematic formula