Monodromy and Kawai-Lewellen-Tye Relations for Gravity Amplitudes

We are still learning intriguing new facets of the string theory motivated Kawai-Lewellen-Tye (KLT) relations linking products of amplitudes in Yang-Mills theories and amplitudes in gravity. This is very clearly displayed in computations of N=8 supergravity where the perturbative expansion show a vast number of similarities to that of N=4 super-Yang-Mills. We will here investigate how identities based on monodromy relations for Yang-Mills amplitudes can be very useful for organizing and further streamlining the KLT relations yielding even more compact results for gravity amplitudes.Comment: 6 pages, 12th Marcel Grossman meeting 200

String theory and the KLT-relations between gravity and gauge theory including external matter

We consider the Kawai-Lewellen-Tye (KLT) factorizations of gravity scalar-leg amplitudes into products of scalar-leg Yang-Mills amplitudes. We check and examine the factorizations at O(1) in $\alpha'$ and extend the analysis by considering KLT-mapping in the case of generic effective Lagrangians for Yang-Mills theory and gravity.Comment: 7 pages, ReVTeX4, references updated, changes to text and typos correcte

Explicit Cancellation of Triangles in One-loop Gravity Amplitudes

We analyse one-loop graviton amplitudes in the field theory limit of a genus-one string theory computation. The considered amplitudes can be dimensionally reduced to lower dimensions preserving maximal supersymmetry. The particular case of the one-loop five-graviton amplitude is worked out in detail and explicitly features no triangle contributions. Based on a recursive form of the one-loop amplitude we investigate the contributions that will occur at n-point order in relation to the ``no-triangle'' hypothesis of N=8 supergravity. We argue that the origin of unexpected cancellations observed in gravity scattering amplitudes is linked to general coordinate invariance of the gravitational action and the summation over all orderings of external legs. Such cancellations are instrumental in the extraordinary good ultra-violet behaviour of N=8 supergravity amplitudes and will play a central role in improving the high-energy behaviour of gravity amplitudes at more than one loop.Comment: 25 pages. 2 eps pictures, harvmac format. v2: version to appear in JHEP. Equations (3.9), (3.12) and minor typos correcte

Absence of Triangles in Maximal Supergravity Amplitudes

From general arguments, we show that one-loop n-point amplitudes in colourless theories satisfy a new type of reduction formula. These lead to the existence of cancellations beyond supersymmetry. Using such reduction relations we prove the no-triangle hypothesis in maximal supergravity by showing that in four dimensions the n-point graviton amplitude contain only scalar box integral functions. We also discuss the reduction formulas in the context of gravity amplitudes with less and no supersymmetry.Comment: 23 pages, RevTeX4 format. v2: Expanded version with a new section providing some extra background material and an overview of the general arguments. Minors typos have been corrected. Version to be publishe

Gravitino Interactions from Yang-Mills Theory

We fabricate gravitino vertex interactions using as only input on-shell Yang-Mills amplitudes and the Kawai-Lewellen-Tye gauge theory / gravity relations. A useful result of this analysis is simpler tree-level Feynman rules for gravitino scattering than in traditional gauges. All results are explicitly verified until five point scattering.Comment: 17 pages, 10 figures, REVTe

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

Similarities of gauge and gravity amplitudes

We review recent progress in computations of amplitudes in gauge theory and gravity. We compare the perturbative expansion of amplitudes in N=4 super Yang-Mills and N=8 supergravity and discuss surprising similarities.Comment: Talk presented by Harald Ita at "Continuous Advances in QCD 2006", 7 page

On-shell Techniques and Universal Results in Quantum Gravity

We compute the leading post-Newtonian and quantum corrections to the Coulomb and Newtonian potentials using the full modern arsenal of on-shell techniques; we employ spinor-helicity variables everywhere, use the Kawai-Lewellen-Tye (KLT) relations to derive gravity amplitudes from gauge theory and use unitarity methods to extract the terms needed at one-loop order. We stress that our results are universal and thus will hold in any quantum theory of gravity with the same low-energy degrees of freedom as we are considering. Previous results for the corrections to the same potentials, derived historically using Feynman graphs, are verified explicitly, but our approach presents a huge simplification, since starting points for the computations are compact and tedious index contractions and various complicated integral reductions are eliminated from the onset, streamlining the derivations. We also analyze the spin dependence of the results using the KLT factorization, and show how the spinless correction in the framework are easily seen to be independent of the interacting matter considered.Comment: 34 pages, 7 figures, typos corrected, published versio

Perturbative Gravity and Twistor Space

The recent progress in computing gauge theory amplitudes can be extended, in many cases, to theories incorporating gravity. This has improved our understanding of the perturbative expansion of N=8 supergravity supporting the ``no-triangle hypothesis'' that N=8 one-loop amplitudes may be expressed in terms of scalar box integral functions.Comment: Talk presented by N. E. J. Bjerrum-Bohr at Loop and Legs 2006, 5 page

New Factorization Relations for Yang Mills Amplitudes

A double-cover extension of the scattering equation formalism of Cachazo, He and Yuan (CHY) leads us to conjecture covariant factorization formulas of n-particle scattering amplitudes in Yang-Mills theories. Evidence is given that these factorization relations are related to Berends-Giele recursions through repeated use of partial fraction identities involving linearized propagators.Comment: 7 pages, 3 figures, version to appear in PR