1,333 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
Leading quantum gravitational corrections to QED
We consider the leading post-Newtonian and quantum corrections to the
non-relativistic scattering amplitude of charged spin-1/2 fermions in the
combined theory of general relativity and QED. The coupled Dirac-Einstein
system is treated as an effective field theory. This allows for a consistent
quantization of the gravitational field. The appropriate vertex rules are
extracted from the action, and the non-analytic contributions to the 1-loop
scattering matrix are calculated in the non-relativistic limit. The
non-analytical parts of the scattering amplitude are known to give the long
range, low energy, leading quantum corrections, are used to construct the
leading post-Newtonian and quantum corrections to the two-particle
non-relativistic scattering matrix potential for two massive fermions with
electric charge.Comment: 14 pages, 29 figures, format RevTex
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
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
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
Time transients in the quantum corrected Newtonian potential induced by a massless nonminimally coupled scalar field
We calculate the one loop graviton vacuum polarization induced by a massless,
nonminimally coupled scalar field on Minkowski background. We make use of the
Schwinger-Keldysh formalism, which allows us to study time dependent phenomena.
As an application we compute the leading quantum correction to the Newtonian
potential of a point particle. The novel aspect of the calculation is the use
of the Schwinger-Keldysh formalism, within which we calculate the time
transients induced by switching on of the graviton-scalar coupling.Comment: 22 pages, 5 figures; detailed calculation of the graviton vacuum
polarization moved to the new Appendix; matches published versio
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
Low-lying spectra in anharmonic three-body oscillators with a strong short-range repulsion
Three-body Schroedinger equation is studied in one dimension. Its two-body
interactions are assumed composed of the long-range attraction (dominated by
the L-th-power potential) in superposition with a short-range repulsion
(dominated by the (-K)-th-power core) plus further subdominant power-law
components if necessary. This unsolvable and non-separable generalization of
Calogero model (which is a separable and solvable exception at L = K = 2) is
presented in polar Jacobi coordinates. We derive a set of trigonometric
identities for the potentials which generalizes the well known K=2 identity of
Calogero to all integers. This enables us to write down the related partial
differential Schroedinger equation in an amazingly compact form. As a
consequence, we are able to show that all these models become separable and
solvable in the limit of strong repulsion.Comment: 18 pages plus 6 pages of appendices with new auxiliary identitie
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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