24 research outputs found
Einstein-Yang-Mills from pure Yang-Mills amplitudes
We present new relations for scattering amplitudes of color ordered gluons
and gravitons in Einstein-Yang-Mills theory. Tree-level amplitudes of arbitrary
multiplicities and polarizations involving up to three gravitons and up to two
color traces are reduced to partial amplitudes of pure Yang-Mills theory. In
fact, the double-trace identities apply to Einstein-Yang-Mills extended by a
dilaton and a B-field. Our results generalize recent work of Stieberger and
Taylor for the single graviton case with a single color trace. As the
derivation is made in the dimension-agnostic Cachazo-He-Yuan formalism, our
results are valid for external bosons in any number of spacetime dimensions.
Moreover, they generalize to the superamplitudes in theories with 16
supercharges.Comment: 28 pages, v2: references and appendix added, published versio
A note on NMHV form factors from the Gra{\ss}mannian and the twistor string
In this note we investigate Gra{\ss}mannian formulas for form factors of the
chiral part of the stress-tensor multiplet in superconformal
Yang-Mills theory. We present an all- contour for the
Gra{\ss}mannian integral of NMHV form factors derived from on-shell diagrams
and the BCFW recursion relation. In addition, we study other
formulas obtained from the connected prescription introduced recently. We find
a recursive expression for all and study its properties. For ,
our formula has the same recursive structure as its amplitude counterpart,
making its soft behaviour manifest. Finally, we explore the connection between
the two Gra{\ss}mannian formulations, using the global residue theorem, and
find that it is much more intricate compared to scattering amplitudes.Comment: 21 pages, 3 figures; v2: JHEP version + minor correction
Celestial Amplitudes: Conformal Partial Waves and Soft Limits
Massless scattering amplitudes in four-dimensional Minkowski spacetime can be
Mellin transformed to correlation functions on the celestial sphere at null
infinity called celestial amplitudes. We study various properties of massless
four-point scalar and gluon celestial amplitudes such as conformal partial wave
decomposition, crossing relations and optical theorem. As a byproduct, we
derive the analog of the single and double soft limits for all gluon celestial
amplitudes.Comment: 13 pages, 1 figur
On-Shell Methods for the Two-Loop Dilatation Operator and Finite Remainders
We compute the two-loop minimal form factors of all operators in the SU(2)
sector of planar N=4 SYM theory via on-shell unitarity methods. From the UV
divergence of this result, we obtain the two-loop dilatation operator in this
sector. Furthermore, we calculate the corresponding finite remainder functions.
Since the operators break the supersymmetry, the remainder functions do not
have the property of uniform transcendentality. However, the leading
transcendentality part turns out to be universal and is identical to the
corresponding BPS expressions. The remainder functions are shown to satisfy
linear relations which can be explained by Ward identities of form factors
following from R-symmetry.Comment: 24 pages; v2: typos corrected, some formulations clarified, matches
published versio
Star Integrals, Convolutions and Simplices
We explore single and multi-loop conformal integrals, such as the ones
appearing in dual conformal theories in flat space. Using Mellin amplitudes, a
large class of higher loop integrals can be written as simple
integro-differential operators on star integrals: one-loop -gon integrals in
dimensions. These are known to be given by volumes of hyperbolic simplices.
We explicitly compute the five-dimensional pentagon integral in full generality
using Schl\"afli's formula. Then, as a first step to understanding higher
loops, we use spline technology to construct explicitly the hexagon and
octagon integrals in two-dimensional kinematics. The fully massive hexagon
and octagon integrals are then related to the double box and triple box
integrals respectively. We comment on the classes of functions needed to
express these integrals in general kinematics, involving elliptic functions and
beyond.Comment: 23 page
A note on NMHV form factors from the Graßmannian and the twistor string
In this note we investigate Graßmannian formulas for form factors of the chiral part of the stress-tensor multiplet in N=4 superconformal Yang-Mills theory. We present an all-n contour for the G(3, n + 2) Graßmannian integral of NMHV form factors derived from on-shell diagrams and the BCFW recursion relation. In addition, we study other G(3, n + 2) formulas obtained from the connected prescription introduced recently. We find a recursive expression for all n and study its properties. For n ≥ 6, our formula has the same recursive structure as its amplitude counterpart, making its soft behaviour manifest. Finally, we explore the connection between the two Graßmannian formulations, using the global residue theorem, and find that it is much more intricate compared to scattering amplitudes
A Grassmannian Etude in NMHV Minors
Arkani-Hamed, Cachazo, Cheung and Kaplan have proposed a Grassmannian
formulation for the S-matrix of N=4 Yang-Mills as an integral over link
variables. In parallel work, the connected prescription for computing tree
amplitudes in Witten's twistor string theory has also been written in terms of
link variables. In this paper we extend the six- and seven-point results of
arXiv:0909.0229 and arXiv:0909.0499 by providing a simple analytic proof of the
equivalence between the two formulas for all tree-level NMHV superamplitudes.
Also we note that a simple deformation of the connected prescription integrand
gives directly the ACCK Grassmannian integrand in the limit when the
deformation parameters equal zero.Comment: 17 page
Note on Bonus Relations for N=8 Supergravity Tree Amplitudes
We study the application of non-trivial relations between gravity tree
amplitudes, the bonus relations, to all tree-level amplitudes in N=8
supergravity. We show that the relations can be used to simplify explicit
formulae of supergravity tree amplitudes, by reducing the known form as a sum
of (n-2)! permutations obtained by solving on-shell recursion relations, to a
new form as a (n-3)!-permutation sum. We demonstrate the simplification by
explicit calculations of the next-to-maximally helicity violating (NMHV) and
next-to-next-to-maximally helicity violating (N^2MHV) amplitudes, and provide a
general pattern of bonus coefficients for all tree-level amplitudes.Comment: 21 pages, 9 figures; v2, minor changes, references adde