Quantum gravity at a large number of dimensions

We consider the large-$D$ limit of Einstein gravity. It is observed that a consistent leading large-$D$ graph limit exists, and that it is built up by a subclass of planar diagrams. The graphs in the effective field theory extension of Einstein gravity are investigated in the same context, and it is seen that an effective field theory extension of the basic Einstein-Hilbert theory will not upset the latter leading large-$D$ graph limit, {\it i.e.}, the same subclass of planar diagrams will dominate at large-$D$ in the effective field theory. The effective field theory description of large-$D$ quantum gravity limit will be renormalizable, and the resulting theory will thus be completely well defined up to the Planck scale at $\sim 10^{19}$ GeV. The $(\frac1D)$ expansion in gravity is compared to the successful $(\frac1N)$ expansion in gauge theory (the planar diagram limit), and dissimilarities and parallels of the two expansions are discussed. We consider the expansion of the effective field theory terms and we make some remarks on explicit calculations of $n$-point functions.Comment: 18 pages, 23 figures (75 files), format RevTex4, typos corrected, references adde

Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program

Using only the Britto-Cachazo-Feng-Witten(BCFW) on-shell recursion relation we prove color-order reversed relation, $U(1)$-decoupling relation, Kleiss-Kuijf(KK) relation and Bern-Carrasco-Johansson(BCJ) relation for color-ordered gauge amplitude in the framework of S-matrix program without relying on Lagrangian description. Our derivation is the first pure field theory proof of the new discovered BCJ identity, which substantially reduces the color ordered basis from $(n-2)!$ to $(n-3)!$. Our proof gives also its physical interpretation as the mysterious bonus relation with ${1\over z^2}$ behavior under suitable on-shell deformation for no adjacent pair.Comment: 4 Pages. No Figures. Rewriting of Introductio

The Complete KLT-Map Between Gravity and Gauge Theories

We present the complete map of any pair of super Yang-Mills theories to supergravity theories as dictated by the KLT relations in four dimensions. Symmetries and the full set of associated vanishing identities are derived. A graphical method is introduced which simplifies counting of states, and helps in identifying the relevant set of symmetries.Comment: 41 pages, 16 figures, published version, typos corrected, references adde

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

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

Generalized string theory mapping relations between gravity and gauge theory

A previous study of the Kawai, Lewellen and Tye (KLT) relations between gravity and gauge theories, imposed by the relationship of closed and open strings, are here extended in the light of general relativity and Yang-Mills theory as effective field theories. We discuss the possibility of generalizing the traditional KLT mapping in this effective setting. A generalized mapping between the effective Lagrangians of gravity and Yang-Mills theory is presented, and the corresponding operator relations between gauge and gravity theories at the tree level are further explored. From this generalized mapping remarkable diagrammatic relations are found, -- linking diagrams in gravity and Yang-Mills theory, -- as well as diagrams in pure effective Yang-Mills theory. Also the possibility of a gravitational coupling to an antisymmetric field in the gravity scattering amplitude is considered, and shown to allow for mixed open-closed string solutions, i.e., closed heterotic strings.Comment: 10 pages, 7 figures, format ReVTeX, comments and ref. added, typos correcte

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

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

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