Theory Colloquium: When a Symmetry Breaks

Spontaneous Symmetry Breaking is a very universal concept applicable for a wide range of subjects: crystal, superfluid, neutron stars, Higgs boson, magnets, and many others. Yet there is a variety in the spectrum of gapless excitations even when the symmetry breaking patterns are the same. We unified all known examples of internal symmetries in a single-line Lagrangian of the low-energy effective theory. In addition, we now have a better understanding of what happens with spacetime symmetries, and predict gaps for certain states
exactly based on symmetries alone.