The Structure of Multiloop Amplitudes in Gauge and Gravity Theories

We review the recently discovered duality between color and kinematics in gauge theories. This duality leads to a remarkably simple double-copy relation between diagrammatic numerators of gravity scattering amplitudes and gauge-theory ones. We summarize nontrivial evidence that the duality and double-copy property holds to all loop orders. We also comment on other developments, including a proof that the gauge-theory duality leads to the gravity double-copy property, and the identification of gauge-theory Lagrangians whose double copies yield gravity Lagrangians.Comment: To appear in Proceedings of Loops and Legs in Quantum Field Theory, Woerlitz, Germany, April 25-30, 2010; 4 figure

Unitarity Cuts: NLO Six-Gluon Amplitudes in QCD

We report on a technique for evaluating finite unitarity cut for one-loop amplitudes in gauge theories, and discuss its application to the cut-constructible part of six-gluon amplitude in QCD.Comment: talk given at Loops & Legs 2006, April 23-28, Eisenach (Germany

Reduction of multi-leg loop integrals

I give an efficient algorithm for the reduction of multi-leg one-loop integrals of rank one. The method combines the basic ideas of the spinor algebra approach with the dual vector approach and is applicable to box integrals or higher point integrals, if at least one external leg is massless. This method does not introduce Gram determinants in the denominator. It completes an algorithm recently given by R. Pittau.Comment: 10 pages, 4 figures, uses axodraw.sty, final version, minor change

Is N = 8 Supergravity Ultraviolet Finite?

Conventional wisdom holds that no four-dimensional gravity field theory can be ultraviolet finite. This understanding is based mainly on power counting. Recent studies confirm that one-loop N = 8 supergravity amplitudes satisfy the so-called `no-triangle hypothesis', which states that triangle and bubble integrals cancel from these amplitudes. A consequence of this hypothesis is that for any number of external legs, at one loop N = 8 supergravity and N = 4 super-Yang-Mills have identical superficial degrees of ultraviolet behavior in D dimensions. We describe how the unitarity method allows us to promote these one-loop cancellations to higher loops, suggesting that previous power counts were too conservative. We discuss higher-loop evidence suggesting that N = 8 supergravity has the same degree of divergence as N = 4 super-Yang-Mills theory and is ultraviolet finite in four dimensions. We comment on calculations needed to reinforce this proposal, which are feasible using the unitarity method.Comment: 7 pages, 5 figures, revte

Amplitudes and Ultraviolet Behavior of N=8 Supergravity

In this contribution we describe computational tools that permit the evaluation of multi-loop scattering amplitudes in N=8 supergravity, in terms of amplitudes in N=4 super-Yang-Mills theory. We also discuss the remarkable ultraviolet behavior of N=8 supergravity, which follows from these amplitudes, and is as good as that of N=4 super-Yang-Mills theory through at least four loops.Comment: 28 pages, 8 figures, 3 tables. Talk presented at XVIth European Workshop on String Theory, Madrid, June, 2010. v2: minor typos fixe

SU(N) group-theory constraints on color-ordered five-point amplitudes at all loop orders

Color-ordered amplitudes for the scattering of n particles in the adjoint representation of SU(N) gauge theory satisfy constraints arising solely from group theory. We derive these constraints for n=5 at all loop orders using an iterative approach. These constraints generalize well-known tree-level and one-loop group theory relations.Comment: 16 pages, no figures; v2: minor corrections and clarifications, published versio

One-Loop Amplitudes in Supersymmetric QCD from MHV Vertices

The Cachazo-Svrcek-Witten (CSW) rule for efficiently calculating gauge theory amplitudes is extended to N=1 supersymmetric QCD (SQCD), incorporating massless quarks, in a way preserving the manifest supersymmetry. Using this extended CSW rule, we obtain compact expressions of all the one-loop MHV amplitudes in SQCD including one or two external quark-antiquark (chiral-antichiral multiplets) pairs. The collinear sigularities of the five point amplitudes are investigated to confirm the consistency of the results.Comment: 43pages,5figures,PTPTex;v2 2references and related footnote are added;v3 English is improved, to appear in Prog. Theor. Phy

One-loop corrections to five-parton amplitudes with external photons

Recently the calculations of all five-parton one-loop QCD amplitudes have been completed. In this letter we describe how to get the corresponding amplitudes with one gluon replaced by a photon and we give the explicit results for the process 0 \to 2q 2Q 1\y.Comment: 7 pages, late

One-Loop Corrections to Two-Quark Three-Gluon Amplitudes

We present the one-loop QCD amplitudes for two external massless quarks and three external gluons ($\bar{q}qggg$). This completes the set of one-loop amplitudes needed for the next-to-leading-order corrections to three-jet production at hadron colliders. We also discuss how to use group theory and supersymmetry to minimize the amount of calculation required for the more general case of one-loop two-quark $n$-gluon amplitudes. We use collinear limits to provide a stringent check on the amplitudes.Comment: plain Tex, 46 pages with 13 figures in a uuencoded file, corrected case j=1 of eq. (IV.7), and signs in eq. (4.9

Self-dual Yang--Mills Theory and One-Loop Maximally Helicity Violating Multi-Gluon Amplitudes

A scalar cubic action that classically reproduces the self-dual Yang--Mills equations is shown to generate one-loop QCD amplitudes for external gluon all with the same helicity. This result is related to the symmetries of the self-dual Yang--Mills equations.Comment: 20 pages, LaTeX2e, elsart, no figures. Final version, to appear in Nucl. Phys. B. Section 3 has been expanded and remodelled. A note has been added to comment on subsequent works by Chalmers and Siegel and Korepin and Oot