3,843 research outputs found
Ambitwistor strings and the scattering equations
We show that string theories admit chiral infinite tension analogues in which
only the massless parts of the spectrum survive. Geometrically they describe
holomorphic maps to spaces of complex null geodesics, known as ambitwistor
spaces. They have the standard critical space--time dimensions of string theory
(26 in the bosonic case and 10 for the superstring). Quantization leads to the
formulae for tree--level scattering amplitudes of massless particles found
recently by Cachazo, He and Yuan. These representations localize the vertex
operators to solutions of the same equations found by Gross and Mende to govern
the behaviour of strings in the limit of high energy, fixed angle scattering.
Here, localization to the scattering equations emerges naturally as a
consequence of working on ambitwistor space. The worldsheet theory suggests a
way to extend these amplitudes to spinor fields and to loop level. We argue
that this family of string theories is a natural extension of the existing
twistor string theories.Comment: 31 pages + refs & appendice
Brane-World Inflation and the Transition to Standard Cosmology
In the context of a five-dimensional brane-world model motivated from
heterotic M-theory, we develop a framework for potential-driven brane-world
inflation. Specifically this involves a classification of the various
background solutions of (A)dS_5 type, an analysis of five-dimensional slow-roll
conditions and a study of how a transition to the flat vacuum state can be
realized. It is shown that solutions with bulk potential and both bane
potentials positive exist but are always non-separating and have a non-static
orbifold. It turns out that, for this class of backgrounds, a transition to the
flat vacuum state during inflation is effectively prevented by the rapidly
expanding orbifold. We demonstrate that such a transition can be realized for
solutions where one boundary potential is negative. For this case, we present
two concrete inflationary models which exhibit the transition explicitly.Comment: 50 pages, 3 figures, minor typos correcte
From Twistor Actions to MHV Diagrams
We show that MHV diagrams are the Feynman diagrams of certain twistor actions
for gauge theories in an axial gauge. The gauge symmetry of the twistor action
is larger than that on space-time and this allows us to fix a gauge that makes
the MHV formalism manifest but which is inaccessible from space-time. The
framework is extended to describe matter fields: as an illustration we
explicitly construct twistor actions for an adjoint scalar with arbitrary
polynomial potential and a fermion in the fundamental representation and show
how this leads to additional towers of MHV vertices in the MHV diagram
formalism.Comment: 12 pages, RevTe
Gravity from Rational Curves
This paper presents a new formula which is conjectured to yield all tree
amplitudes in N=8 supergravity. The amplitudes are described in terms of higher
degree rational maps to twistor space. The resulting expression has manifest
N=8 supersymmetry and is manifestly permutation symmetric in all external
states. It depends monomially on the infinity twistor that explicitly breaks
conformal symmetry to Poincare. The formula has been explicitly checked to
yield the correct amplitudes for the 3-point MHV-bar and for the n-point MHV,
where it reduces to an expression of Hodges. We have also carried out numerical
checks of the formula at NMHV and NNMHV level, for up to eight external states.Comment: 8 page
Gravity in Twistor Space and its Grassmannian Formulation
We prove the formula for the complete tree-level -matrix of
supergravity recently conjectured by two of the authors. The
proof proceeds by showing that the new formula satisfies the same BCFW
recursion relations that physical amplitudes are known to satisfy, with the
same initial conditions. As part of the proof, the behavior of the new formula
under large BCFW deformations is studied. An unexpected bonus of the analysis
is a very straightforward proof of the enigmatic behavior of gravity.
In addition, we provide a description of gravity amplitudes as a
multidimensional contour integral over a Grassmannian. The Grassmannian
formulation has a very simple structure; in the NMHV sector the
integrand is essentially the product of that of an MHV and an amplitude, with and particles respectively
Geographically intelligent disclosure control for flexible aggregation of census data
This paper describes a geographically intelligent approach to disclosure control for protecting flexibly aggregated census data. Increased analytical power has stimulated user demand for more detailed information for smaller geographical areas and customized boundaries. Consequently it is vital that improved methods of statistical disclosure control are developed to protect against the increased disclosure risk. Traditionally methods of statistical disclosure control have been aspatial in nature. Here we present a geographically intelligent approach that takes into account the spatial distribution of risk. We describe empirical work illustrating how the flexibility of this new method, called local density swapping, is an improved alternative to random record swapping in terms of risk-utility
Euler systems for GSp(4)
We construct an Euler system for Galois representations associated to
cohomological cuspidal automorphic representations of the group GSp(4), using
the pushforwards of Eisenstein classes for GL(2) x GL(2).Comment: 41 pages. Revised version -- main theorem now applies in all
cohomological weight
- β¦