199 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
Supersymmetric S-matrices from the worldsheet in 10 and 11d
We obtain compact formulae for tree super-amplitudes for 10 and
11-dimensional supergravity and 10-dimensional supersymmetric Yang-Mills and
Born-Infeld. These are based on the \emph{polarised scattering equations}.
These incorporate polarization data into a spinor field on the Riemann sphere
and arise from a twistorial representation of ambitwistor strings in 10 and 11
dimensions. They naturally extend amplitude formulae to manifest maximal
supersymmetry. The framework is the natural generalization of twistorial
ambitwistor string formulae found previously in four and six dimensions and is
informally motivated from a vertex operator prescription for a family of
supersymmetric worldsheet ambitwistor string models.Comment: 7 page
The polarized scattering equations for 6d superamplitudes
We introduce a spinorial version of the scattering equations, the
\emph{polarized scattering equations}, that incorporates spinor polarization
data. They lead to new formulae for tree-level scattering amplitudes in six
dimensions that directly extend to maximal supersymmetry. They give a quite
distinct framework from that of Cachazo et al.; in particular, the formulae do
not change character from even to odd numbers of particles. We find new
ingredients for integrands for maximally supersymmetric Yang-Mills, gravity, M5
and D5 branes. We explain how the polarized scattering equations and
supersymmetry representations arise from an ambitwistor-string with target
given by a super-twistor description of the geometry of super-ambitwistor space
for six dimensions. On reduction to four dimensions the polarized scattering
equations give rise to massive analogues of the 4d refined scattering equations
for amplitudes on the Coulomb branch. At zero mass this framework naturally
generalizes the twistorial version of the ambitwistor string in four
dimensions.Comment: 13 page
Regularity at space-like and null infinity
We extend Penrose's peeling model for the asymptotic behaviour of solutions
to the scalar wave equation at null infinity on asymptotically flat
backgrounds, which is well understood for flat space-time, to Schwarzschild and
the asymptotically simple space-times of Corvino-Schoen/Chrusciel-Delay. We
combine conformal techniques and vector field methods: a naive adaptation of
the ``Morawetz vector field'' to a conformal rescaling of the Schwarzschild
metric yields a complete scattering theory on Corvino-Schoen/Chrusciel-Delay
space-times. A good classification of solutions that peel arises from the use
of a null vector field that is transverse to null infinity to raise the
regularity in the estimates. We obtain a new characterization of solutions
admitting a peeling at a given order that is valid for both Schwarzschild and
Minkowski space-times. On flat space-time, this allows large classes of
solutions than the characterizations used since Penrose's work. Our results
establish the validity of the peeling model at all orders for the scalar wave
equation on the Schwarzschild metric and on the corresponding
Corvino-Schoen/Chrusciel-Delay space-times
Hyper-K{\"a}hler Hierarchies and their twistor theory
A twistor construction of the hierarchy associated with the hyper-K\"ahler
equations on a metric (the anti-self-dual Einstein vacuum equations, ASDVE, in
four dimensions) is given. The recursion operator R is constructed and used to
build an infinite-dimensional symmetry algebra and in particular higher flows
for the hyper-K\"ahler equations. It is shown that R acts on the twistor data
by multiplication with a rational function. The structures are illustrated by
the example of the Sparling-Tod (Eguchi-Hansen) solution. An extended
space-time is constructed whose extra dimensions correspond to
higher flows of the hierarchy. It is shown that is a moduli space of
rational curves with normal bundle in twistor
space and is canonically equipped with a Lax distribution for ASDVE
hierarchies. The space is shown to be foliated by four dimensional
hyper-K{\"a}hler slices. The Lagrangian, Hamiltonian and bi-Hamiltonian
formulations of the ASDVE in the form of the heavenly equations are given. The
symplectic form on the moduli space of solutions to heavenly equations is
derived, and is shown to be compatible with the recursion operator.Comment: 23 pages, 1 figur
Einstein supergravity amplitudes from twistor-string theory
This paper gives a twistor-string formulation for all tree amplitudes of
Einstein (super-)gravities for N=0 and 4. Formulae are given with and without
cosmological constant and with various possibilities for the gauging. The
formulae are justified by use of Maldacena's observation that conformal gravity
tree amplitudes with Einstein wave functions and non-zero cosmological constant
will correctly give the Einstein tree amplitudes. This justifies the
construction of Einstein gravity amplitudes at N=0 from twistor-string theory
and is extended to N=4 by requiring the standard relation between the
MHV-degree and the degree of the rational curve for Yang-Mills; this
systematically excludes the spurious conformal supergravity gravity
contributions. For comparison, BCFW recursion is used to obtain
twistor-string-like formulae at degree zero and one (anti-MHV and MHV) for
amplitudes with N=8 supersymmetry with and without cosmological constant.Comment: 20 pages. v2: minor corrections & clarification of relation to
formulae of Maldacena & Pimentel and Raju; v3: appendix on BCFW recursion
added, published version. v4: Full derivation for 3 point MHV amplitude now
include
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
Twistor Construction of Higher-Dimensional Black Holes - Part II: Examples
We apply the twistor construction for higher-dimensional black holes to known
examples in five space-time dimensions. First the patching matrices are
calculated from the explicit metric for these examples. Then an ansatz is
proposed for obtaining the patching matrix instead from the data of rod
structure and angular momenta. The ansatz is tested on examples with up to
three nuts, and these are shown to give flat space, the Myers-Perry solution
and the black ring, as expected. Rules for the transition between different
adaptations of the patching matrix and for the elimination of conical
singularities are developed and seen to work.Comment: 35 pages, 5 figure
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
Gravity from holomorphic discs and celestial symmetries
In split or Kleinian signature, twistor constructions parametrize solutions
to both gauge and gravity self-duality (SD) equation from twistor data that can
be expressed in terms of free smooth data without gauge freedom. Here the
corresponding constructions are given for asymptotically flat SD gravity
providing a fully nonlinear encoding of the asymptotic gravitational data in
terms of a real homogeneous generating function on the real twistor space.
Geometrically determines a nonlinear deformation of the location of the
real twistor space \RP^3 inside the complex twistor space \CP^3.
This presentation gives an optimal presentation of Strominger's recently
discovered celestial symmetries. These, when real, act locally
as passive Poisson diffeomorphisms on the real twistor space. However, when
imaginary, such Poisson transformations are active symmetries, and generate
changes to the gravitational field by deforming the location of the real slice
of the twistor space.
Gravity amplitudes for the full, non-self-dual Einstein gravity, arise as
correlators of a chiral twistor sigma model. This is reformulated for split
signature as a theory of holomorphic discs in twistor space whose boundaries
lie on the deformed real slice determined by . Real
symmetries act oas gauge symmetries, but imaginary generators yield graviton
vertex operators that generate gravitons in the perturbative expansion.
A generating function for the all plus 1-loop amplitude, an analogous
framework for Yang-Mills, possible interpretations in Lorentz signature and
similar open string formulations of twistor and ambitwistor strings in 4d in
split signature, are briefly discussed.Comment: 26 pages, 2 figures and appendice
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