On rolling, tunneling and decaying in some large N vector models

TL;DR

This paper investigates time-dependent phenomena such as rolling, tunneling, and decay in large N O(N) vector models in three dimensions, providing exact solutions and analyzing the effects of time dependence on effective potentials.

Contribution

It offers exact and approximate solutions for dynamic processes in large N vector models, including a numerical analysis of tunneling with thick bubble walls.

Findings

Characteristic times are shorter with time-dependent effective potentials.

Different approximation methods agree in overlapping validity regions.

Numerical solutions show thick-walled tunneling bubbles.

Abstract

Various aspects of time-dependent processes are studied within the large N approximation of O(N) vector models in three dimensions. These include the rolling of fields, the tunneling and decay of vacua. We present an exact solution for the quantum conformal case and find a solution for more general potentials when the total change of the value of the field is small. Characteristic times are found to be shorter when the time dependence of the field is taken into account in constructing the exact large N effective potentials. We show that the different approximations yield the same answers in the regions of the overlap of the validity. A numerical solution of this potential reveals a tunneling in which the bubble that separates the true vacuum from the false one is thick.