26 research outputs found
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
Four photon production at the LHC: an application of 2->4 analytic unitarity
We present Next-to-Leading Order (NLO) predictions for
final states, including the effects of photon
fragmentation. Our results are calculated fully analytically using the
techniques of -dimensional unitarity, and we discuss some refinements to
existing methods, focusing particularly on the role of three-mass triangle
coefficients. Using these techniques we are able to produce a numerically
stable Monto Carlo code that runs fully in double precision. We investigate the
signal at colliders, both for Run II of the LHC and at future
machines. Our results are implemented in MCFM.Comment: 12 pages, 5 figures, 1 tabl
Landau Singularities from the Amplituhedron
We propose a simple geometric algorithm for determining the complete set of
branch points of amplitudes in planar N=4 super-Yang-Mills theory directly from
the amplituhedron, without resorting to any particular representation in terms
of local Feynman integrals. This represents a step towards translating
integrands directly into integrals. In particular, the algorithm provides
information about the symbol alphabets of general amplitudes. We illustrate the
algorithm applied to the one- and two-loop MHV amplitudes.Comment: 34 pages, 16 figures; v2: minor corrections and improvement
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
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