(2,0) Theory and Higher Spin: Twisting, Turning and Spinning Towards Higher Energies

This thesis investigates an enigmatic six-dimensional quantum theory known as (2,0) theory and a three dimensional conformal theory of higher spin. The former has resisted an explicit construction as a quantum field theory, yet its existence can be inferred from string theory and M-theory where it plays a prominent role. Theories of higher spin, only recently emerging with consistent formulations, also have intricate connections with string theory where they might provide insight into the high energy behaviour and have recently played an important part in holographic dualities. A deeper understanding of these theories is therefore an important challange that promise to provide new insight into string theory and the mathematical framework of theoretical physics in general.First the six dimensional (2,0) theory is investigated in terms of an explicit formulation of one free tensor multiplet on circle fibrations. The fibration geometry provides additional data in a compactification to five dimensions used to derive an interacting generalization. Topological twisting of the tensor multiplet is then carried out, resulting in an off-shell formulation making use of the Q-cohomology structure.The second part of the thesis concerns conformal higher spin in three dimensions, constructed as an extension of the gauge theory formulation of gravity. Using a computer tensor algebra system developed for this purpose, the full non-linear system is solved at the spin 3 level