19 research outputs found
Supersymmetric Gauge Theories in Twistor Space
We construct a twistor space action for N=4 super Yang-Mills theory and show
that it is equivalent to its four dimensional spacetime counterpart at the
level of perturbation theory. We compare our partition function to the original
twistor-string proposal, showing that although our theory is closely related to
string theory, it is free from conformal supergravity. We also provide twistor
actions for gauge theories with N<4 supersymmetry, and show how matter
multiplets may be coupled to the gauge sector.Comment: 23 pages, no figure
Solitons and admissible families of rational curves in twistor spaces
It is well known that twistor constructions can be used to analyse and to
obtain solutions to a wide class of integrable systems. In this article we
express the standard twistor constructions in terms of the concept of an
admissible family of rational curves in certain twistor spaces. Examples of of
such families can be obtained as subfamilies of a simple family of rational
curves using standard operations of algebraic geometry. By examination of
several examples, we give evidence that this construction is the basis of the
construction of many of the most important solitonic and algebraic solutions to
various integrable differential equations of mathematical physics. This is
presented as evidence for a principal that, in some sense, all soliton-like
solutions should be constructable in this way.Comment: 15 pages, Abstract and introduction rewritten to clarify the
objectives of the paper. This is the final version which will appear in
Nonlinearit
Scattering Amplitudes and BCFW Recursion in Twistor Space
Twistor ideas have led to a number of recent advances in our understanding of
scattering amplitudes. Much of this work has been indirect, determining the
twistor space support of scattering amplitudes by examining the amplitudes in
momentum space. In this paper, we construct the actual twistor scattering
amplitudes themselves. We show that the recursion relations of Britto, Cachazo,
Feng and Witten have a natural twistor formulation that, together with the
three-point seed amplitudes, allows us to recursively construct general tree
amplitudes in twistor space. We obtain explicit formulae for -particle MHV
and NMHV super-amplitudes, their CPT conjugates (whose representations are
distinct in our chiral framework), and the eight particle N^2MHV
super-amplitude. We also give simple closed form formulae for the N=8
supergravity recursion and the MHV and conjugate MHV amplitudes. This gives a
formulation of scattering amplitudes in maximally supersymmetric theories in
which superconformal symmetry and its breaking is manifest. For N^kMHV, the
amplitudes are given by 2n-4 integrals in the form of Hilbert transforms of a
product of purely geometric, superconformally invariant twistor delta
functions, dressed by certain sign operators. These sign operators subtly
violate conformal invariance, even for tree-level amplitudes in N=4 super
Yang-Mills, and we trace their origin to a topological property of split
signature space-time. We develop the twistor transform to relate our work to
the ambidextrous twistor diagram approach of Hodges and of Arkani-Hamed,
Cachazo, Cheung and Kaplan.Comment: v2: minor corrections + extra refs. v3: further minor corrections,
extra discussion of signature issues + more ref
Gravity, Twistors and the MHV Formalism
We give a self-contained derivation of the MHV amplitudes for gravity and use
the associated twistor generating function to define a twistor action for the
MHV diagram approach to gravity. Starting from a background field calculation
on a spacetime with anti self-dual curvature, we obtain a simple spacetime
formula for the scattering of a single, positive helicity linearized graviton
into one of negative helicity. Re-expressing our integral in terms of twistor
data allows us to consider a spacetime that is asymptotic to a superposition of
plane waves. Expanding these out perturbatively yields the gravitational MHV
amplitudes of Berends, Giele & Kuijf. We go on to take the twistor generating
function off-shell at the perturbative level. Combining this with a twistor
action for the anti self-dual background, we obtain a twistor action for the
MHV diagram approach to perturbative gravity. We finish by extending these
results to supergravity, in particular N=4 and N=8.Comment: 39 pages, 3 figures. Minor typos corrected, some clarification adde