156 research outputs found
Explicit BCJ Numerators from Pure Spinors
We derive local kinematic numerators for gauge theory tree amplitudes which
manifestly satisfy Jacobi identities analogous to color factors. They naturally
emerge from the low energy limit of superstring amplitudes computed with the
pure spinor formalism. The manifestation of the color--kinematics duality is a
consequence of the superstring computation involving no more than (n-2)!
kinematic factors for the full color dressed n-point amplitude. The bosonic
part of these results describe gluon scattering independent on the number of
supersymmetries and captures any N^kMHV helicity configuration after
dimensional reduction to D=4 dimensions.Comment: 32 pages, harvma
The Structure of n-Point One-Loop Open Superstring Amplitudes
In this article we present the worldsheet integrand for one-loop amplitudes
in maximally supersymmetric superstring theory involving any number n of
massless open string states. The polarization dependence is organized into the
same BRST invariant kinematic combinations which also govern the leading string
correction to tree level amplitudes. The dimensions of the bases for both the
kinematics and the associated worldsheet integrals is found to be the unsigned
Stirling number S_3^{n-1} of first kind. We explain why the same combinatorial
structures govern on the one hand finite one-loop amplitudes of equal helicity
states in pure Yang Mills theory and on the other hand the color tensors at
quadratic alpha prime order of the color dressed tree amplitude.Comment: 75 pp, 8 figs, harvmac TeX, v2: published versio
Towards Field Theory Amplitudes From the Cohomology of Pure Spinor Superspace
A simple BRST-closed expression for the color-ordered super-Yang-Mills
5-point amplitude at tree-level is proposed in pure spinor superspace and shown
to be BRST-equivalent to the field theory limit of the open superstring 5-pt
amplitude. It is manifestly cyclic invariant and each one of its five terms can
be associated to the five Feynman diagrams which use only cubic vertices. Its
form also suggests an empirical method to find superspace expressions in the
cohomology of the pure spinor BRST operator for higher-point amplitudes based
on their kinematic pole structure. Using this method, Ansaetze for the 6- and
7-point 10D super-Yang-Mills amplitudes which map to their 14 and 42
color-ordered diagrams are conjectured and their 6- and 7-gluon expansions are
explicitly computed.Comment: 14 pages, harvmac, v4: trivial edits in the text to comply with JHEP
refere
A New Proposal for the Picture Changing Operators in the Minimal Pure Spinor Formalism
Using a new proposal for the "picture lowering" operators, we compute the
tree level scattering amplitude in the minimal pure spinor formalism by
performing the integration over the pure spinor space as a multidimensional
Cauchy-type integral. The amplitude will be written in terms of the projective
pure spinor variables, which turns out to be useful to relate rigorously the
minimal and non-minimal versions of the pure spinor formalism. The natural
language for relating these formalisms is the Cech-Dolbeault isomorphism.
Moreover, the Dolbeault cocycle corresponding to the tree-level scattering
amplitude must be evaluated in SO(10)/SU(5) instead of the whole pure spinor
space, which means that the origin is removed from this space. Also, the
Cech-Dolbeault language plays a key role for proving the invariance of the
scattering amplitude under BRST, Lorentz and supersymmetry transformations, as
well as the decoupling of unphysical states. We also relate the Green's
function for the massless scalar field in ten dimensions to the tree-level
scattering amplitude and comment about the scattering amplitude at higher
orders. In contrast with the traditional picture lowering operators, with our
new proposal the tree level scattering amplitude is independent of the constant
spinors introduced to define them and the BRST exact terms decouple without
integrating over these constant spinors.Comment: 56 pages, typos correcte
One-loop SYM-supergravity relation for five-point amplitudes
We derive a linear relation between the one-loop five-point amplitude of N=8
supergravity and the one-loop five-point subleading-color amplitudes of N=4
supersymmetric Yang-Mills theory.Comment: 17 pages, 2 figures; v2: very minor correction
The Overall Coefficient of the Two-loop Superstring Amplitude Using Pure Spinors
Using the results recently obtained for computing integrals over
(non-minimal) pure spinor superspace, we compute the coefficient of the
massless two-loop four-point amplitude from first principles. Contrasting with
the mathematical difficulties in the RNS formalism where unknown normalizations
of chiral determinant formulae force the two-loop coefficient to be determined
only indirectly through factorization, the computation in the pure spinor
formalism can be smoothly carried out.Comment: 29 pages, harvmac TeX. v2: add reference
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
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