206 research outputs found
Proof of Gravity and Yang-Mills Amplitude Relations
Using BCFW on-shell recursion techniques, we prove a sequence of explicit
n-point Kawai-Lewellen-Tye relations between gravity and Yang-Mills amplitudes
at tree level.Comment: 17 pages, no figures, JHE
Colour-kinematics duality and the Drinfeld double of the Lie algebra of diffeomorphisms
Colour-kinematics duality suggests that Yang-Mills (YM) theory possesses some hidden Lie algebraic structure. So far this structure has resisted understanding, apart from some progress in the self-dual sector. We show that there is indeed a Lie algebra behind the YM Feynman rules. The Lie algebra we uncover is the Drinfeld double of the Lie algebra of vector fields. More specifically, we show that the kinematic numerators following from the YM Feynman rules satisfy a version of the Jacobi identity, in that the Jacobiator of the bracket defined by the YM cubic vertex is cancelled by the contribution of the YM quartic vertex. We then show that this Jacobi-like identity is in fact the Jacobi identity of the Drinfeld double. All our considerations are off-shell. Our construction explains why numerators computed using the Feynman rules satisfy the colour-kinematics at four but not at higher numbers of points. It also suggests a way of modifying the Feynman rules so that the duality can continue to hold for an arbitrary number of gluons. Our construction stops short of producing explicit higher point numerators because of an absence of a certain property at four points. We comment on possible ways of correcting this, but leave the next word in the story to future work
On tree amplitudes with gluons coupled to gravitons
In this paper, we study the tree amplitudes with gluons coupled to gravitons.
We first study the relations among the mixed amplitudes. With BCFW on-shell
recursion relation, we will show the color-order reversed relation,
-decoupling relation and KK relation hold for tree amplitudes with gluons
coupled to gravitons. We then study the disk relation which expresses mixed
amplitudes by pure gluon amplitudes. More specifically we will prove the disk
relation for mixed amplitudes with gluons coupled to one graviton. Using the
disk relation and the properties of pure gluon amplitudes, the color-order
reversed relation, -decoupling relation and KK relation for mixed
amplitudes can also be proved. Finally, we give some brief discussions on
BCJ-like relation for mixed amplitudes.Comment: 33pages,no figur
The Momentum Kernel of Gauge and Gravity Theories
We derive an explicit formula for factorizing an -point closed string
amplitude into open string amplitudes. Our results are phrased in terms of a
momentum kernel which in the limit of infinite string tension reduces to the
corresponding field theory kernel. The same momentum kernel encodes the
monodromy relations which lead to the minimal basis of color-ordered amplitudes
in Yang-Mills theory. There are interesting consequences of the momentum kernel
pertaining to soft limits of amplitudes. We also comment on surprising links
between gravity and certain combinations of kinematic and color factors in
gauge theory.Comment: 19 pages, 1 figur
The Kinematic Algebra From the Self-Dual Sector
We identify a diffeomorphism Lie algebra in the self-dual sector of
Yang-Mills theory, and show that it determines the kinematic numerators of
tree-level MHV amplitudes in the full theory. These amplitudes can be computed
off-shell from Feynman diagrams with only cubic vertices, which are dressed
with the structure constants of both the Yang-Mills colour algebra and the
diffeomorphism algebra. Therefore, the latter algebra is the dual of the colour
algebra, in the sense suggested by the work of Bern, Carrasco and Johansson. We
further study perturbative gravity, both in the self-dual and in the MHV
sectors, finding that the kinematic numerators of the theory are the BCJ
squares of the Yang-Mills numerators.Comment: 29 pages, 5 figures. v2: references added, published versio
BCJ Relation of Color Scalar Theory and KLT Relation of Gauge Theory
We present a field theoretical proof of the conjectured KLT relation which
states that the full tree-level scattering amplitude of gluons can be written
as a product of color-ordered amplitude of gluons and color-ordered amplitude
of scalars with only cubic vertex. To give a proof we establish the KK relation
and BCJ relation of color-ordered scalar amplitude using BCFW recursion
relation with nonzero boundary contributions. As a byproduct, an off-shell
version of fundamental BCJ relation is proved, which plays an important role in
our work.Comment: 26 pages, 9 figure
Note on New KLT relations
In this short note, we present two results about KLT relations discussed in
recent several papers. Our first result is the re-derivation of Mason-Skinner
MHV amplitude by applying the S_{n-3} permutation symmetric KLT relations
directly to MHV amplitude. Our second result is the equivalence proof of the
newly discovered S_{n-2} permutation symmetric KLT relations and the well-known
S_{n-3} permutation symmetric KLT relations. Although both formulas have been
shown to be correct by BCFW recursion relations, our result is the first direct
check using the regularized definition of the new formula.Comment: 15 Pages; v2: minor correction
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