Symmetries in gravity and supergravity in the light cone gauge

Abstract

This thesis examines the symmetries in gravity and supergravity in four dimensionsin the light cone gauge The initial focus of the thesis is revisiting pure gravity in fourdimensions in the light cone gauge We describe how the light cone Hamiltonian forpure gravity can be expressed as a positive definite quadratic form We also discusssecond order corrections to residual reparametrizations which leave the light coneHamiltonian invariant We comment on possible links this quadratic form structuremight have to hidden symmetries in gravity This is in light of some recent studieswhich suggest improved ultraviolet behaviour in pure gravity The second part of the thesis examines the symmetries in maximal supergravitytheories which is our key focus The maximal supergravity theory in four dimensions N 8 supergravity has excellent ultraviolet properties not all of which can betraced back to the known symmetries in the theory We first study the symmetriesof N 8 supergravity in the light cone superspace We then argue that the theorypossesses a larger symmetry than previously believed The proof involves dimensionalreduction of the theory to three dimensions a field redefinition in d 3 and oxidationback to d 4 Finally we extend our analysis to d 11 to argue that there is ahidden exceptional symmetry in eleven dimensional supergravity We explain howthe exceptional symmetries in these theories are as fundamental as supersymmetry itself newline newline