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

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

Absence of Three-Loop Four-Point Divergences in N=4 Supergravity

We compute the coefficient of the potential three-loop divergence in pure N=4 supergravity and show that it vanishes, contrary to expectations from symmetry arguments. The recently uncovered duality between color and kinematics is used to greatly streamline the calculation. We comment on all-loop cancellations hinting at further surprises awaiting discovery at higher loops.Comment: 5 pages, 3 figures; v2 added references and minor correction

An R^4 non-renormalisation theorem in N=4 supergravity

We consider the four-graviton amplitudes in CHL constructions providing four-dimensional N=4 models with various numbers of vector multiplets. We show that in these models the two-loop amplitude has a prefactor of d^2R^4. This implies a non-renormalisation theorem for the R^4 term, which forbids the appearance of a three-loop ultraviolet divergence in four dimensions in the four-graviton amplitude. We connect the special nature of the R^4 term to the U(1) anomaly of pure N=4 supergravity.Comment: v2: added comments about one-loop UV divergences. Assorted stylistic corrections. Added references. v3: Eq. III.21 corrected and assorted minor corrections and clarifications. Version to be published. v4: minor corrections. 18 pages. one figur