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 $n$-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