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

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

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

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

Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory

By exploiting relations between gravity and gauge theories, we present two infinite sequences of one-loop n-graviton scattering amplitudes: the `maximally helicity-violating' amplitudes in N=8 supergravity, and the `all-plus' helicity amplitudes in gravity with any minimally coupled massless matter content. The all-plus amplitudes correspond to self-dual field configurations and vanish in supersymmetric theories. We make use of the tree-level Kawai-Lewellen-Tye (KLT) relations between open and closed string theory amplitudes, which in the low-energy limit imply relations between gravity and gauge theory tree amplitudes. For n < 7, we determine the all-plus amplitudes explicitly from their unitarity cuts. The KLT relations, applied to the cuts, allow us to extend to gravity a previously found `dimension-shifting' relation between (the cuts of) the all-plus amplitudes in gauge theory and the maximally helicity-violating amplitudes in N=4 super-Yang-Mills theory. The gravitational version of the relation lets us determine the n < 7 N=8 supergravity amplitudes from the all-plus gravity amplitudes. We infer the two series of amplitudes for all n from their soft and collinear properties, which can also be derived from gauge theory using the KLT relations.Comment: Minor errors corrected, Latex, 53 page

Numerical evaluation of phase space integrals by sector decomposition

In a series of papers we have developed the method of iterated sector decomposition for the calculation of infrared divergent multi-loop integrals. Here we apply it to phase space integrals to calculate a contribution to the double real emission part of the e+e- -> 2 jets cross section at NNLO. The explicit cancellation of infrared poles upon summation over all possible cuts of a given topology is worked out in detail for a specific example.Comment: 15 pages, 2 figure

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

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

Evolution Kernels from Splitting Amplitudes

We recalculate the next-to-leading order Altarelli-Parisi kernel using a method which relates it to the splitting amplitudes describing the collinear factorization properties of scattering amplitudes. The method breaks up the calculation of the kernel into individual pieces which have an independent physical interpretation.Comment: References adde

One-Loop Amplitudes for e^+ e^- to Four Partons

We present the first explicit formulae for the complete set of one-loop helicity amplitudes necessary for computing next-to-leading order corrections for e^+ e^- annihilation into four jets, for W, Z or Drell-Yan production in association with two jets at hadron colliders, and for three-jet production in deeply inelastic scattering experiments. We include a simpler form of the previously published amplitudes for e^+ e^- to four quarks. We obtain the amplitudes using their analytic properties to constrain their form. Systematically eliminating spurious poles from the amplitudes leads to relatively compact results.Comment: Tex, 82 pages, Maple and Mathematica files containing the amplitudes are available from the author