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

The rational parts of one-loop QCD amplitudes II: The five-gluon case

The rational parts of 5-gluon one-loop amplitudes are computed by using the newly developed method for computing the rational parts directly from Feynman integrals. We found complete agreement with the previously well-known results of Bern, Dixon and Kosower obtained by using the string theory method. Intermediate results for some combinations of Feynman diagrams are presented in order to show the efficiency of the method and the local cancellation between different contributions.Comment: 25 pages, 16 figures and LaTeX file; minor corrections, references added, to be published in Nucl. Phys.

Recursive Approach to One-loop QCD Matrix Elements

We describe the recursive Approach to One-loop QCD Matrix Elements.Comment: 6 pages, to appear in the proceedings of the 7th International Symposium on Radiative Corrections: Application of Quantum Field Theory to Phenomenology (RADCOR 2005), Japan, 2-7 Oct 200

Ultra-Violet Infinities and Counterterms in Higher Dimensional Yang-Mills

In this letter we investigate the ultra-violet behaviour of four-point one-loop gluon amplitudes in dimensions greater than four coupled to various particles types. We discuss the structure of the counterterms and their inherent symmetries.Comment: 14 pages, LateX, axodra

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

The Infrared Behavior of One-Loop Gluon Amplitudes at Next-to-Next-to-Leading Order

For the case of $n$-jet production at next-to-next-to-leading order in the QCD coupling, in the infrared divergent corners of phase space where particles are collinear or soft, one must evaluate $(n+1)$-parton final-state one-loop amplitudes through \Ord(\eps^2), where \eps is the dimensional regularization parameter. For the case of gluons, we present to all orders in \eps the required universal functions which describe the behavior of one-loop amplitudes in the soft and collinear regions of phase space. An explicit example is discussed for three-parton production in multi-Regge kinematics that has applications to the next-to-leading logarithmic corrections to the BFKL equation.Comment: Latex, 14 pages, no figure

On Perturbative Gravity and Gauge Theory

We review some applications of tree-level (classical) relations between gravity and gauge theory that follow from string theory. Together with $D$-dimensional unitarity, these relations can be used to perturbatively quantize gravity theories, i.e. they contain the necessary information for obtaining loop contributions. We also review recent applications of these ideas showing that N=1 D=11 supergravity diverges, and review arguments that N=8 D=4 supergravity is less divergent than previously thought, though it does appear to diverge at five loops. Finally, we describe field variables for the Einstein-Hilbert Lagrangian that help clarify the perturbative relationship between gravity and gauge theory.Comment: Talk presented at Third Meeting on Constrained Dynamics and Quantum Gravity, Villasimius (Sardinia, Italy) September 13-17, 1999 and at the Workshop on Light-Cone QCD and Nonperturbative Hadron Physics, University of Adelaide (Australia) December 13-22, 1999. Latex, 9 page

Calculation of 1-loop Hexagon Amplitudes in the Yukawa Model

We calculate a class of one-loop six-point amplitudes in the Yukawa model. The construction of multi-particle amplitudes is done in the string inspired formalism and compared to the Feynman diagrammatic approach. We show that there exists a surprisingly efficient way of calculating such amplitudes by using cyclic identities of kinematic coefficients and discuss in detail cancellation mechanisms of spurious terms. A collection of formulas which are useful for the calculation of massless hexagon amplitudes is given.Comment: 15 pages Late

Exploiting Twistor Techniques for One-loop QCD Amplitudes

In this talk we describe the recursive Approach to One-loop QCD Matrix Elements.Comment: Talk presented by David C. Dunbar at Loop and Legs 2006, 5 page

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