The homogeneity theorem for supergravity backgrounds

We prove the strong homogeneity conjecture for eleven- and ten-dimensional (Poincar\'e) supergravity backgrounds. In other words, we show that any backgrounds of 11-dimensional, type I/heterotic or type II supergravity theories preserving a fraction greater than one half of the supersymmetry of the underlying theory are necessarily locally homogeneous. Moreover we show that the homogeneity is due precisely to the supersymmetry, so that at every point of the spacetime one can find a frame for the tangent space made out of Killing vectors constructed out of the Killing spinors.Comment: 8 page

Lorentzian Lie n-algebras

We classify Lie n-algebras possessing an invariant lorentzian inner product.Comment: 10 pages (V2: more details on Section 3 and a new lemma. V3: typos corrected

License to Kill: An Analysis of the Legality of Fully Autonomous Drones in the Context of International Use of Force Law

We live in a world of constant technological change; and with this change, comes unknown effects and consequences. This is even truer with weapons and warfare. Indeed, as the means and methods of warfare rapidly modify and transform, the effects and consequences on the laws of war are unknown. This Article addresses one such development in weapon and warfare technology—Fully Autonomous Weapons or “Killer Robots”—and discusses the inevitable use of these weapons within the current international law framework. Recognizing the current, inadequate legal framework, this Article proposes a regulation policy to mitigate the risks associated with Fully Autonomous Weapons. But the debate should not end here; States and the U.N. must work together to adopt a legal framework that coincides with the advancement of technology. This Article starts that discussion

N=2 structures in all string theories

The BRST cohomology of any topological conformal field theory admits the structure of a Batalin--Vilkovisky algebra, and string theories are no exception. Let us say that two topological conformal field theories are ``cohomologically equivalent'' if their BRST cohomologies are isomorphic as Batalin--Vilkovisky algebras. What we show in this paper is that any string theory (regardless of the matter background) is cohomologically equivalent to some twisted N=2 superconformal field theory. We discuss three string theories in detail: the bosonic string, the NSR string and the W_3 string. In each case the way the cohomological equivalence is constructed can be understood as coupling the topological conformal field theory to topological gravity. These results lend further supporting evidence to the conjecture that _any_ topological conformal field theory is cohomologically equivalent to some topologically twisted N=2 superconformal field theory. We end the paper with some comments on different notions of equivalence for topological conformal field theories and this leads to an improved conjecture.Comment: 23 pages (12 physical pages), .dvi.uu (+ some hyperlinks