Soft Theorems from Spontaneous Symmetry Breaking

Spontaneous symmetry breaking occurs when the vacuum state is not preserved under (a subset of) symmetries in the theory. Instead, the symmetry is non-linearly realized by the associated massless degrees of freedom, the Nambu-Goldstone bosons. At the level of on-shell observables, the non-linearly realized symmetry is manifested as a universal structure of scattering amplitudes in the so-called soft limit, which means sending the momenta of a Nambu-Goldstone modes to zero. In this dissertation, we further explore the link between spontaneous symmetry breaking and infrared dynamics of massless scalars. First, we derive soft theorems for theories with spontaneously broken Poincaré symmetries, corresponding to effective field theories for condensed matter systems such as solids, fluids, superfluids, and framids. We also implement a bootstrap in which the enhanced vanishing of amplitudes in the soft limit is taken as an input, thus sculpting out a subclass of exceptional solid, fluid, and framid theories. Next, we consider spontaneous breaking of higher symmetries. We derive a new sub-leading double soft pion theorem in theories with a spontaneously-broken continuous 2-group global symmetry, which intertwines amplitudes with different numbers of pions and photons. We also provide a novel derivation of the leading soft photon theorem from the Ward identity of an emergent 1-form global symmetry in effective field theories where antiparticles are integrated out. Finally, we turn to universal features in low-energy dynamics of generic effective field theories. We extend the scalar geometric soft theorem by allowing the massless scalar to couple to other scalars, fermions, and gauge bosons. The soft theorem keeps its geometric form, but where the field-space geometry now involves the full field content of the theory. As a bonus, we also present novel double soft theorems with fermions, which mimic the geometric structure of the double soft theorem for scalars.