Abstract:
This thesis examines the symmetries in gravity and supergravity in four dimensions
in the light-cone gauge. The initial focus of the thesis is revisiting pure gravity in four
dimensions in the light-cone gauge. We describe how the light-cone Hamiltonian for
pure gravity can be expressed as a positive definite quadratic form. We also discuss
second-order corrections to residual reparametrizations, which leave the light-cone
Hamiltonian invariant. We comment on possible links this quadratic form structure
might have to hidden symmetries in gravity. This is in light of some recent studies
which suggest improved ultraviolet behaviour in pure gravity.
The second part of the thesis examines the symmetries in maximal supergravity
theories, which is our key focus. The maximal supergravity theory in four dimensions,
N = 8 supergravity, has excellent ultraviolet properties, not all of which can be
traced back to the known symmetries in the theory. We first study the symmetries
of N = 8 supergravity in the light-cone superspace. We then argue that the theory
possesses a larger symmetry than previously believed. The proof involves dimensional
reduction of the theory to three dimensions, a field redefinition in d = 3 and oxidation
back to d = 4. Finally, we extend our analysis to d = 11 to argue that there is a
hidden exceptional symmetry in eleven-dimensional supergravity. We explain how
the exceptional symmetries in these theories are as fundamental as supersymmetry
itself.
