Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop

We show that the four-loop four-point amplitudes of N = 5 supergravity are ultraviolet finite in four dimensions, contrary to expectations based on supersymmetry and duality-symmetry arguments. We explain why the diagrams of any covariant local formalism cannot manifestly exhibit the necessary cancellations for finiteness but instead require a new type of nontrivial ultraviolet cancellation that we call "enhanced cancellations". We also show that the three-loop four-point amplitudes in N = 4 and N = 5 supergravity theories display enhanced cancellations. To construct the loop integrand, we use the duality between color and kinematics. We apply standard methods for extracting ultraviolet divergences in conjunction with the FIRE5 integral reduction program to arrive at the four-loop results.Comment: 26 pages,8 figures, RevTe

Fabrication of Pd-Cr wire

Fabrication of Pd-13 percent Cr alloy wires is described. Melting, casting, swaging and annealing processes are discussed. Drawing to reach two diameters (0.003 inch and 0.00176 inch) of wire is described. Representative micrographs of the Pd-Cr alloy at selected stages during wire fabrication are included. The resistance of the wire was somewhat lower, by about 15 to 20 percent, than comparable wire of other alloys used for strain gages

Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops

We provide evidence in favor of the conjectured duality between color and kinematics for the case of nonsupersymmetric pure Yang-Mills amplitudes by constructing a form of the one-loop four-point amplitude of this theory that makes the duality manifest. Our construction is valid in any dimension. We also describe a duality-satisfying representation for the two-loop four-point amplitude with identical four-dimensional external helicities. We use these results to obtain corresponding gravity integrands for a theory containing a graviton, dilaton, and antisymmetric tensor, simply by replacing color factors with specified diagram numerators. Using this, we give explicit forms of ultraviolet divergences at one loop in four, six, and eight dimensions, and at two loops in four dimensions.Comment: 35 page, 10 figures, REVTex, ancillary mathematica file containing one-loop diagram numerators, latest version includes updated references, corrected two-loop numerators and various clarification

Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure

We show that the double-copy structure of gravity forbids divergences in pure half-maximal (16 supercharge) supergravity at four and five points at one loop in D<8 and at two loops in D<6. We link the cancellations that render these supergravity amplitudes finite to corresponding ones that eliminate forbidden color factors from the divergences of pure nonsupersymmetric Yang-Mills theory. The vanishing of the two-loop four-point divergence in D=5 half-maximal supergravity is an example where a valid counterterm satisfying the known symmetries exists, yet is not present. We also give explicit forms of divergences in half-maximal supergravity at one loop in D=8 and at two loops in D=6.Comment: 32 pages, revtex, 6 figures, v3 minor correction