| dc.description.abstract | Scattering amplitudes of massless quanta play a crucial role in the calculation of
cross sections for multi-jet production at hadron colliders. The framework provided by
perturbative quantum field theory, based on Feynman diagrams, does not capture their
simplicity, as it breaks some of the symmetries of the theory at the diagrammatic level.
Consequently, vast cancellations give rise to strikingly simple mathematical expressions
representing the amplitudes. These theoretical motivations and experimental needs
have stimulated the search for new techniques for calculating efficiently scattering
amplitudes. In particular, a new diagrammatic method of calculation, now known as
the “MHV diagram method”, was developed, and many intriguing results were found
for the maximally supersymmetric N = 4 Yang-Mills theory.
In this thesis we explore these remarkable properties, extending many of the results
to the gravitational counterpart of maximally supersymmetric Yang-Mills theory,
N = 8 supergravity. In particular we develop the MHV diagram method for the
calculation of graviton amplitudes at one loop. We rederive explicitly the four- and
five-point MHV amplitude of gravitons at one loop, in agreement with known results,
and outline the procedure for the extension of this technique to the case of an arbitrary
number of gravitons. We then investigate possible iterative structures in the
higher-loop expansion of N = 8 supergravity, extending the exponentiation of infrared
divergences. Finally, we discuss possible definitions of Wilson loops in supergravity,
and put forward a proposal for a new duality, analogous to the duality in N = 4 super
Yang-Mills, between perturbative scattering amplitudes and the expectation value of
certain lightlike polygonal Wilson loops. | en_US |
