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CHY Formulae and Soft Theorems in N = 4 Super Yang-Mills Theory
PhDThe study of scattering amplitudes in quantum eld theories (QFTs) is equally important
for high energy phenomenology and for theoretical understanding of fundamental
physics. Over the last 15 years there has been an explosion of new techniques, inspired
by Witten's celebrated twistor string theory [1]. The N = 4 super Yang-Mills theory
(SYM) provides a playground for applying and extending these methods, heavily
constrained by spacetime, internal and hidden symmetries.
Recently, Cachazo, He and Yuan proposed an algebraic construction of scattering amplitudes
at tree level in various QFTs, based on the solution of certain scattering equations
[2]. This formula was later extended to tree-level form factors of Tr(F2
SD) in four
dimensional Yang-Mills theory [3]. In this thesis we show how this result may be naturally
supersymmetrised, and derived from a dual connected formulation. Moreover, we
relate our results to a geometric construction of form factors via the Grassmannian [4].
Finally, we argue that ambitwistor string theory provides a natural way to lift the result
to arbitrary dimensions, paving the way for loop-level results.
In complementary work, it was shown that the subleading soft behaviour of tree-level
amplitudes in gauge theory and gravity is universal [5{7]. This unexpected property
is related to extended symmetries of the theory acting at null in nity. Moreover, the
hidden structure provides additional information relevant for resummation of physical
observables. In this thesis, we extend the known results to one-loop level in N = 4
SYM, arguing that IR divergences introduce anomaly terms through nite order in the
regulator. We constrain these terms using dual superconformal symmetry, and derive
explicit formulae in the MHV and NMHV sectors.
This thesis contains documentation for two Mathematica packages, illustrating the
original calculations we have performed.STFC studentship