119 research outputs found
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
Twistor actions for gauge theory and gravity
This is a review of recent developments in the study of perturbative gauge
theory and gravity using action functionals on twistor space. It is intended to
provide a user-friendly introduction to twistor actions, geared towards
researchers or graduate students interested in learning something about the
utility, prospects, and shortcomings of this approach. For those already
familiar with the twistor approach, it should provide a condensed overview of
the literature as well as several novel results of potential interest. This
work is based primarily upon the author's D.Phil. thesis. We first consider
four-dimensional, maximally supersymmetric Yang-Mills theory as a gauge theory
in twistor space. We focus on the perturbation theory associated to this
action, which in an axial gauge leads to the MHV formalism. This allows us to
efficiently compute scattering amplitudes at tree-level (and beyond) in twistor
space. Other gauge theory observables such as local operators and null
polygonal Wilson loops can also be formulated twistorially, leading to proofs
for several correspondences between correlation functions and Wilson loops, as
well as a recursive formula for computing mixed Wilson loop / local operator
correlators. We then apply the twistor action approach to general relativity,
using the on-shell equivalence between conformal and Einstein gravity. This can
be extended to N=4 supersymmetry. The perturbation theory of the twistor action
leads to formulae for the MHV amplitude with and without cosmological constant,
yields a candidate for the Einstein twistor action, and induces a MHV formalism
on twistor space. Appendices include discussion of super-connections and
Coulomb branch regularization on twistor space.Comment: 178 pages, 30 figures. Review based on the author's D.Phil. thesis.
v2: references adde
Bethe-Salpeter equation for classical gravitational bound states
The Bethe-Salpeter equation is a non-perturbative, relativistic and covariant
description of two-body bound states. We derive the classical Bethe-Salpeter
equation for two massive point particles (with or without spin) in a bound
gravitational system. This is a recursion relation which involves
two-massive-particle-irreducible diagrams in the space of classical amplitudes,
defined by quotienting out by symmetrization over internal graviton exchanges.
In this context, we observe that the leading eikonal approximation to two-body
scattering arises directly from unitarity techniques with a coherent state of
virtual gravitons. More generally, we solve the classical Bethe-Salpeter
equation analytically at all orders by exponentiating the classical kernel in
impact parameter space. We clarify the connection between this classical kernel
and the Hamilton-Jacobi action, making manifest the analytic continuation
between classical bound and scattering observables. Using explicit analytic
resummations of classical (spinless and spinning) amplitudes in momentum space,
we further explore the relation between poles with bound state energies and
residues with bound state wavefunctions. Finally, we discuss a relativistic
analogue of Sommerfeld enhancement which occurs for bound state cross sections.Comment: 45 pages + references, 19 figure
Classical double copy at null infinity
We give two double copy prescriptions which construct asymptotically flat
solutions in gravity from asymptotically flat gauge fields. The first
prescription applies to radiative fields, which are non-linear vacuum solutions
determined by characteristic data at null infinity. For any two such radiative
gauge fields (linear or non-linear), the characteristic data of a radiative
metric, dilaton and axion is constructed by a simple `squaring' procedure,
giving a classical double copy at the level of radiation fields. We demonstrate
the procedure with several examples where the characteristic data can be
explicitly integrated; for linear fields this also sheds light on the
twistorial description of Weyl double copy. Our second prescription applies to
all asymptotically flat fields at the level of their asymptotic equations of
motion: we give a map between any solution of the asymptotic Maxwell equations
and any solution of the asymptotic Einstein equations at null infinity. This
also extends to the asymptotic charges and their duals, preserves the soft and
hard sectors between gauge theory and gravity, and is related to the usual
notion of double copy in scattering amplitudes.Comment: 44 pages, 2 figures. v2: additions to references and discussio
General relativity as a two-dimensional CFT
The tree-level scattering amplitudes of general relativity encode the full
non-linearity of the Einstein field equations. Yet remarkably compact
expressions for these amplitudes have been found which seem unrelated to a
perturbative expansion of the Einstein-Hilbert action. This suggests an
entirely different description of GR which makes this on-shell simplicity
manifest. Taking our cue from the tree-level amplitudes, we discuss how such a
description can be found. The result is a formulation of GR in terms of a
solvable two-dimensional CFT, with the Einstein equations emerging as quantum
consistency conditions.Comment: 6 pages, no figures. Honorable Mention in the 2015 Gravity Research
Foundation Essay Competitio
Twistor sigma models for quaternionic geometry and graviton scattering
We reformulate the twistor construction for hyper- and quaternion-Kähler manifolds, introducing new sigma models that compute scalar potentials for the geometry. These sigma models have the twistor space of the quaternionic manifold as their target and encode finite non-linear perturbations of the flat structures. In the hyperkähler case our twistor sigma models compute both Plebanski fundamental forms (including the Kähler potential), while in the quaternion-Kähler setting the twistor sigma model computes the Kähler potential for the hyperkähler structure on non-projective twistor space. In four-dimensions, one of the models provides the generating functional of tree-level MHV graviton scattering amplitudes; perturbations of the hyperkähler structure corresponding to positive helicity gravitons. The sigma model's perturbation theory gives rise to a sum of tree diagrams observed previously in the literature, and their summation via a matrix tree theorem gives a first-principles derivation of Hodges' formula for MHV graviton amplitudes directly from general relativity. We generalise the twistor sigma model to higher-degree (defined in the first case with a cosmological constant), giving a new generating principle for the full tree-level graviton S-matrix
Infrared structures of scattering on self-dual radiative backgrounds
The scattering of gluons and gravitons in trivial backgrounds is endowed with
many surprising infrared features which have interesting conformal
interpretations on the two-dimensional celestial sphere. However, the fate of
these structures in more general asymptotically flat backgrounds is far from
clear. In this paper, we consider holomorphic infrared structures in the
presence of non-perturbative, self-dual background gauge and gravitational
fields which are determined by freely specified radiative data. We make use of
explicit formulae for tree-level gluon and graviton scattering in these
self-dual radiative backgrounds, as well as chiral twistor sigma model
descriptions of the classical dynamics. Remarkably, we find that the leading
holomorphic part of tree-level collinear splitting functions -- or celestial
OPEs -- and infinite-dimensional chiral soft algebras are undeformed by the
background. We also compute all-order holomorphic celestial OPEs in the MHV
sectors of gauge theory and gravity.Comment: 36+10 pages, no figure
Celestial amplitudes and conformal soft theorems
Scattering amplitudes in dimensions can be expressed in terms of a
conformal basis, for which the S-matrix behaves as a CFT correlation function
on the celestial -sphere. We explain how compact expressions for the full
tree-level S-matrix of gauge theory, gravity and other QFTs extend to this
conformal basis, and are easily derived from ambitwistor strings. Using these
formulae and their worldsheet origins, we prove various tree-level 'conformal
soft theorems' in gauge theory and gravity in any dimension; these arise from
limits where the scaling dimension of an external state in the scattering
process takes special values. These conformally soft limits are obscure from
standard methods, but they are easily derived with ambitwistor strings.
Additionally, we make an identification between the residues of conformally
soft vertex operator insertions in ambitwistor strings and charges generating
asymptotic symmetries.Comment: 18+6 pages, no figures. v2: typos corrected; v3: published versio
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