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

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

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

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

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

On tree amplitudes with gluons coupled to gravitons

In this paper, we study the tree amplitudes with gluons coupled to gravitons. We first study the relations among the mixed amplitudes. With BCFW on-shell recursion relation, we will show the color-order reversed relation, $U(1)$-decoupling relation and KK relation hold for tree amplitudes with gluons coupled to gravitons. We then study the disk relation which expresses mixed amplitudes by pure gluon amplitudes. More specifically we will prove the disk relation for mixed amplitudes with gluons coupled to one graviton. Using the disk relation and the properties of pure gluon amplitudes, the color-order reversed relation, $U(1)$-decoupling relation and KK relation for mixed amplitudes can also be proved. Finally, we give some brief discussions on BCJ-like relation for mixed amplitudes.Comment: 33pages,no figur

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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