44 research outputs found
A Color Dual Form for Gauge-Theory Amplitudes
Recently a duality between color and kinematics has been proposed, exposing a
new unexpected structure in gauge theory and gravity scattering amplitudes.
Here we propose that the relation goes deeper, allowing us to reorganize
amplitudes into a form reminiscent of the standard color decomposition in terms
of traces over generators, but with the role of color and kinematics swapped.
By imposing additional conditions similar to Kleiss-Kuijf relations between
partial amplitudes, the relationship between the earlier form satisfying the
duality and the current one is invertible. We comment on extensions to loop
level.Comment: 5 pages, 4 figure
Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
We demonstrate that the tree-level amplitudes of maximal super-Yang-Mills
theory in six dimensions, when stripped of their overall momentum and
supermomentum delta functions, are covariant with respect to the
six-dimensional dual conformal group. Using the generalized unitarity method,
we demonstrate that this property is also present for loop amplitudes. Since
the six-dimensional amplitudes can be interpreted as massive four-dimensional
ones, this implies that the six-dimensional symmetry is also present in the
massively regulated four-dimensional maximal super-Yang-Mills amplitudes.Comment: 20 pages, 3 figures, minor clarification, references update
The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM
We provide an analytic formula for the (rescaled) one-loop scalar hexagon
integral with all external legs massless, in terms of classical
polylogarithms. We show that this integral is closely connected to two
integrals appearing in one- and two-loop amplitudes in planar
super-Yang-Mills theory, and . The derivative of
with respect to one of the conformal invariants yields
, while another first-order differential operator applied to
yields . We also introduce some kinematic
variables that rationalize the arguments of the polylogarithms, making it easy
to verify the latter differential equation. We also give a further example of a
six-dimensional integral relevant for amplitudes in
super-Yang-Mills.Comment: 18 pages, 2 figure
Amplitudes for Multiple M5 Branes
We study N=(m,0) super-Poincare invariant six-dimensional massless and
five-dimensional massive on-shell amplitudes. We demonstrate that in six
dimensions, all possible three-point amplitudes involving tensor multiplets are
necessarily embedded in gravitational theories. For non-gravitational
amplitudes we consider instead five-dimensional massive amplitudes with N=(2,0)
supersymmetry, aiming at describing the world volume theory of multiple M5
branes compactified on M^{4,1}x S^1. We find non-gravitational amplitudes whose
on-shell degrees of freedom are shown to match those of the massive particle
states that arise from self-dual strings wrapping a circle. Along the way we
find interesting hints of a fermionic symmetry in the (2,0) theory, which
accompanies the self-dual tensor gauge symmetry. We also discuss novel theories
with (3,0) and (4,0) supersymmetry.Comment: 49 pages, 4 figures, v2: Better organization and more details in the
section on KK interaction
Simple superamplitudes in higher dimensions
We provide simple superspaces based on a formulation of spinor helicity in
general even dimensions. As a distinguishing feature these spaces admit a
fermionic super-momentum conserving delta function solution to the on-shell
supersymmetry Ward identities. Using these solutions, we present beautifully
simple formulae for the complete three, four and five point superamplitudes in
maximal super Yang-Mills theory in eight dimensions, and for the three and four
point superamplitudes in ten dimensional type IIB supergravity. In addition, we
discuss the exceptional kinematics of the three point amplitude, and the
supersymmetric spinorial BCFW recursion, in general dimensions.Comment: 34 page
Integrands for QCD rational terms and N=4 SYM from massive CSW rules
We use massive CSW rules to derive explicit compact expressions for
integrands of rational terms in QCD with any number of external legs.
Specifically, we present all-n integrands for the one-loop all-plus and
one-minus gluon amplitudes in QCD. We extract the finite part of spurious
external-bubble contributions systematically; this is crucial for the
application of integrand-level CSW rules in theories without supersymmetry. Our
approach yields integrands that are independent of the choice of CSW reference
spinor even before integration.
Furthermore, we present a recursive derivation of the recently proposed
massive CSW-style vertex expansion for massive tree amplitudes and loop
integrands on the Coulomb-branch of N=4 SYM. The derivation requires a careful
study of boundary terms in all-line shift recursion relations, and provides a
rigorous (albeit indirect) proof of the recently proposed construction of
massive amplitudes from soft-limits of massless on-shell amplitudes. We show
that the massive vertex expansion manifestly preserves all holomorphic and half
of the anti-holomorphic supercharges, diagram-by-diagram, even off-shell.Comment: 30 pages, many figure
Dualities for Loop Amplitudes of N=6 Chern-Simons Matter Theory
In this paper we study the one- and two-loop corrections to the four-point
amplitude of N=6 Chern-Simons matter theory. Using generalized unitarity
methods we express the one- and two-loop amplitudes in terms of dual-conformal
integrals. Explicit integration by using dimensional reduction gives vanishing
one-loop result as expected, while the two-loop result is non-vanishing and
matches with the Wilson loop computation. Furthermore, the two-loop correction
takes the same form as the one-loop correction to the four-point amplitude of
N=4 super Yang-Mills. We discuss possible higher loop extensions of this
correspondence between the two theories. As a side result, we extend the method
of dimensional reduction for three dimensions to five dimensions where dual
conformal symmetry is most manifest, demonstrating significant simplification
to the computation of integrals.Comment: 32 pages and 6 figures. v2: minus sign corrections, ref updated v3:
Published versio
Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions
The spinor helicity formalism in four dimensions has become a very useful
tool both for understanding the structure of amplitudes and also for practical
numerical computation of amplitudes. Recently, there has been some discussion
of an extension of this formalism to higher dimensions. We describe a
particular implementation of the spinor-helicity method in ten dimensions.
Using this tool, we study the tree-level S-matrix of ten dimensional super
Yang-Mills theory, and prove that the theory enjoys a dual conformal symmetry.
Implications for four-dimensional computations are discussed.Comment: 24 pages, 1 figure