Classification of symmetry breaking patterns in the theory of non-linear realizations

Symmetry is a crucial concept in physics. Many of the great revolutions in physics since the time of Newton were both based on principles of symmetry and led to new insights into the role of symmetry in physics. We may distinguish linearly realized symmetries from non-linearly realized symmetries, which lead to different consequences. Linearly realized symmetries determine what kind of particles we can expect to find in colliders and lead to important conserved quantities such as energy and momentum. Non-linearly realized symmetries lead to constraints on the dynamics of particles, but tell us nothing about how to classify fundamental particle states.

The range of possibilities for linear symmetries was understood a long time ago by Coleman and Mandula. However, a classification of all possible non-linearly realized symmetries is lacking. In this thesis, we attempt to make progress in this direction. We focus on non-linear space-time symmetries in relativistic and supersymmetric field theories, using the theory of non-linear realizations. We are able to exhaustively classify so-called exceptional EFTs realized on the most commonly encountered particles of relativistic and supersymmetric physics.