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

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

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

Scattering Equations and String Theory Amplitudes

Scattering equations for tree-level amplitudes are viewed in the context of string theory. As a result of the comparison we are led to define a new dual model which coincides with string theory in both the small and large $\alpha'$ limit, and whose solution is found algebraically on the surface of solutions to the scattering equations. Because it has support only on the scattering equations, it can be solved exactly, yielding a simple resummed model for $\alpha'$-corrections to all orders. We use the same idea to generalize scattering equations to amplitudes with fermions and any mixture of scalars, gluons and fermions. In all cases checked we find exact agreement with known results.Comment: v2: 18 pp, 1 figure, added clarifications and comments. Version to be published in PR

Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes

We discuss monodromy relations between different color-ordered amplitudes in gauge theories. We show that Jacobi-like relations of Bern, Carrasco and Johansson can be introduced in a manner that is compatible with these monodromy relations. The Jacobi-like relations are not the most general set of equations that satisfy this criterion. Applications to supergravity amplitudes follow straightforwardly through the KLT-relations. We explicitly show how the tree-level relations give rise to non-trivial identities at loop level.Comment: 28 pages, 8 figures, JHEP

Minimal Basis for Gauge Theory Amplitudes

Identities based on monodromy for integrations in string theory are used to derive relations between different color ordered tree-level amplitudes in both bosonic and supersymmetric string theory. These relations imply that the color ordered tree-level n-point gauge theory amplitudes can be expanded in a minimal basis of (n-3)! amplitudes. This result holds for any choice of polarizations of the external states and in any number of dimensions.Comment: v2: typos corrected, some rephrasing of the general discussion. Captions to figures added. Version to appear in PRL. 4 pages, 5 figure

Four-Point One-Loop Amplitude Computation in the Pure Spinor Formalism

The massless 4-point one-loop amplitude computation in the pure spinor formalism is shown to agree with the computation in the RNS formalism.Comment: 10 pages harvmac te

Non-renormalization conditions for four-gluon scattering in supersymmetric string and field theory

The constraints imposed by maximal supersymmetry on multi-loop contributions to the scattering of four open superstrings in the U(N) theory are examined by use of the pure spinor formalism. The double-trace term k^2 t_8(tr F^2)^2 (where k represents an external momentum and F the Yang--Mills field strength) only receives contributions from L<=2 (where L is the loop number) while the single-trace term k^2 t_8(tr F^4) receives contributions from all L. We verified these statements up to L=5, but arguments based on supersymmetry suggest they extend to all L. This explains why the single-trace contributions to low energy maximally supersymmetric Yang--Mills field theory are more divergent in the ultraviolet than the double-trace contributions. We also comment further on the constraints on closed string amplitudes and their implications for ultraviolet divergences in N=8 supergravity.Comment: 25 pages. 2 eps figures. Harvmac format. v2 qualifications regarding comments on closed strings. References adde