Bounce Configuration from Gradient Flow
  Based on the gradient flow, we propose a new method to determine the bounce
configuration for false vacuum decay. Our method is applicable to a large class
of models with multiple fields. Since the bounce is a saddle point of an
action, a naive gradient flow method which minimizes the action does not work.
We point out that a simple modification of the flow equation can make the
bounce its stable fixed point while the false vacuum configuration an unstable
one. Consequently, the bounce configuration can be obtained simply by following
the flow without a careful choice of an initial configuration. With numerical
analysis, we confirm the validity of our claim, checking that the flow equation
we propose indeed has solutions that flow into the bounce configuration.
