Vertex-resummed kinetic theory of dipole-symmetric bosons from 2PI effective action

Abstract

The formalism of non-equilibrium dynamics for the dipole-symmetric $U(N)$ model involving $N$-component charged scalar fields is studied on the Schwinger-Keldysh contour by a systematic $1/N$ expansion of two-particle-irreducible (2PI) effective action to the next-to-leading order (NLO). The differential equations describing non-equilibrium evolution equations of two-point functions and field expectation values related to the symmetry breaking in the dynamics are derived, which encompass scatterings between modes essential in the late-time evolution and thermalization beyond the scope of the mean field. At the late-time regime of the evolution, the leading-order (LO) gradient expansion is performed to construct the vertex-resummed kinetic theory by encoding non-perturbative effects in the vertex through the resummation, which is distinct from the standard kinetic theory written by the weak-coupling expansion.