Spontaneous symmetry breaking of gapless fermions as diagnostic: From quantum matter to quantum gravity

Synopsis

Gapless fermionic degrees of freedom abound in nature. On one hand, they can arise as quasiparticles in systems with Fermi points, such as semimetals. On the other hand, all elementary particles known so far are practically massless - at least when compared to the one "natural" mass scale, the Planck mass. The gaplessness of these excitations usually derives from some symmetry, emergent or fundamental. In this talk, I shall illustrate how studying the possible spontaneous breakdown of said symmetries can yield some theoretical insights into the host systems that would otherwise be hard, if not impossible, to come by.