On perturbative scattering amplitudes in maximally supersymmetric theories
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There has been substantial calculational progress in the last few years in maximally
supersymmetric theories, revealing unexpected simplicity, new structures and symmetries.
In this thesis, after reviewing some of the recent advances in N = 4 super
Yang-Mills and N = 8 supergravity, we present calculations of perturbative scattering
amplitudes and polygonal lightlike Wilson loops that lead to interesting new
results.
In N = 8 supergravity, we use supersymmetric generalised unitarity to calculate
supercoe cients of box functions in the expansion of scattering amplitudes at one
loop. Recent advances have presented tree-level amplitudes in N = 8 supergravity
in terms of sums of terms containing squares of colour-ordered Yang-Mills superamplitudes.
We develop the consequences of these results for the structure of one-loop
supercoe cients, recasting them as sums of squares of N = 4 Yang-Mills expressions
with certain coe cients inherited from the tree-level superamplitudes. This
provides new expressions for all one-loop box coe cients in N = 8 supergravity,
which we check against known results in a number of cases.
In N = 4 super Yang-Mills, we focus our attention on one of the many remarkable
features of MHV scattering amplitudes, their conjectured duality to lightlike
polygon Wilson loops, which is expected to hold to all orders in perturbation theory.
This duality is usually expressed in terms of purely four-dimensional quantities
obtained by appropriate subtraction of the infrared and ultraviolet divergences from
amplitudes and Wilson loops respectively. By explicit calculation, we demonstrate
the completely unanticipated fact that the equality continues to hold at two loops
through O( ) in dimensional regularisation for both the four-particle amplitude and
the (parity-even part of the) ve-particle amplitude.
Authors
Katsaroumpas, PanagiotisCollections
- Theses [4352]