7 research outputs found
The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
We give a representation of the parity-even part of the planar two-loop
six-gluon MHV amplitude of N=4 super-Yang-Mills theory, in terms of
loop-momentum integrals with simple dual conformal properties. We evaluate the
integrals numerically in order to test directly the ABDK/BDS all-loop ansatz
for planar MHV amplitudes. We find that the ansatz requires an additive
remainder function, in accord with previous indications from strong-coupling
and Regge limits. The planar six-gluon amplitude can also be compared with the
hexagonal Wilson loop computed by Drummond, Henn, Korchemsky and Sokatchev in
arXiv:0803.1466 [hep-th]. After accounting for differing singularities and
other constants independent of the kinematics, we find that the Wilson loop and
MHV-amplitude remainders are identical, to within our numerical precision. This
result provides non-trivial confirmation of a proposed n-point equivalence
between Wilson loops and planar MHV amplitudes, and suggests that an additional
mechanism besides dual conformal symmetry fixes their form at six points and
beyond.Comment: 49 pages, RevTex, 2 figure file, v2 minor correction
Integrable spin chains and scattering amplitudes
In this review we show that the multi-particle scattering amplitudes in N=4
SYM at large Nc and in the multi-Regge kinematics for some physical regions
have the high energy behavior appearing from the contribution of the Mandelstam
cuts in the complex angular momentum plane of the corresponding t-channel
partial waves. These Mandelstam cuts or Regge cuts are resulting from gluon
composite states in the adjoint representation of the gauge group SU(Nc). In
the leading logarithmic approximation (LLA) their contribution to the six point
amplitude is in full agreement with the known two-loop result.
The Hamiltonian for the Mandelstam states constructed from n gluons in LLA
coincides with the local Hamiltonian of an integrable open spin chain. We
construct the corresponding wave functions using the integrals of motion and
the Baxter-Sklyanin approach.Comment: Invited review for a special issue of Journal of Physics A devoted to
"Scattering Amplitudes in Gauge Theories", R. Roiban(ed), M. Spradlin(ed), A.
Volovich (ed
Generic multiloop methods and application to N=4 super-Yang-Mills
We review some recent additions to the tool-chest of techniques for finding
compact integrand representations of multiloop gauge-theory amplitudes -
including non-planar contributions - applicable for N=4 super-Yang-Mills in
four and higher dimensions, as well as for theories with less supersymmetry. We
discuss a general organization of amplitudes in terms of purely cubic graphs,
review the method of maximal cuts, as well as some special D-dimensional
recursive cuts, and conclude by describing the efficient organization of
amplitudes resulting from the conjectured duality between color and kinematic
structures on constituent graphs.Comment: 42 pages, 18 figures, invited review for a special issue of Journal
of Physics A devoted to "Scattering Amplitudes in Gauge Theories", v2 minor
corrections, v3 added reference
One-loop derivation of the Wilson polygon - MHV amplitude duality
We discuss the origin of the Wilson polygon - MHV amplitude duality at the
perturbative level. It is shown that the duality for the MHV amplitudes at
one-loop level can be proven upon the peculiar change of variables in Feynman
parametrization and the use of the relation between Feynman integrals at the
different space-time dimensions. Some generalization of the duality which
implies the insertion of the particular vertex operator at the Wilson triangle
is found for the 3-point function. We discuss analytical structure of Wilson
loop diagrams and present the corresponding Landau equations. The geometrical
interpretation of the loop diagram in terms of the hyperbolic geometry is
discussed.Comment: 29 page