Goldstone bosons across thermal phase transitions

Abstract

Temperature has a significant effect on the properties of quantum field theories (QFTs) with a spontaneously broken symmetry, in particular on the massless Goldstone bosons that exist in the vacuum state. It has recently been shown using lattice calculations for a $\mathrm{U}(1)$ complex scalar field theory that the Goldstone mode persists even when the symmetry is restored above the critical temperature $T_c$, and has the properties of a screened excitation, a so-called thermoparticle. In this work, we continue the investigation of this theory by determining explicitly how the Goldstone mode evolves as the temperature is increased both below and above $T_c$. We find that the two phases of the theory are entirely characterised by the thermal dissipative effects experienced by the Goldstone mode, with the broken and symmetry-restored phases associated with weak and strong damping, respectively. These findings are consistent with the non-perturbative constraints imposed by spontaneous symmetry breaking, and provide a new way in which to characterise thermal phase transitions in QFTs.

18 pages, 5 figures; v2: additional discussion added, matches published version. Figure data attached