Analyzing multifield tunneling with exact bounce solutions

Abstract

We study multifield tunneling using exact solutions for additive potentials. We introduce a binomial potential with noninteger powers that could be considered a generalization of the 4D Fubini instanton potential. Using scaling arguments, we show that for multifield potentials taller and wider barriers may still lead to a smaller bounce action.

A fresh look at the calculation of tunneling actions in multi-field potentials

“…Projection of Eq. (28) along the path gives again (20): if δφ ∝ dφ one is not really changing the path but V t instead, so one recovers the same equation obtained by varying V t . In essence, the problem formulated using the new action (22) is two-fold: find a path φ(ϕ) and a tunneling potential V t (ϕ) that minimize the action with the boundary conditions:…”

“…which is the EoM in (20). Next, consider the stationarity of the action under variations of the path φ.…”

Tunneling in theories with many fields

“…In [12], it was noted that some aspects of these results could be understood with certain assumptions about the distributions of quartic couplings. Here we point out that the first two of these results can be understood by simple statistical reasoning.…”

“…Ref. [12,13] noted that if the quartic couplings grew like N 2 and the cubic like N 3/2 , one could account for these scaling laws. But simply thinking in terms of random walks such growth is hard to explain.…”

“…Simple scaling arguments give 12) where φ 0 is the bounce for the potential V = φ 2 − φ 3 , and the bounce action scales as µ 2 /γ 2 . Sarid [14] has studied this problem numerically, obtaining…”