Classical Transitions for Flux Vacua

We present the simplest model for classical transitions in flux vacua. A complex field with a spontaneously broken U(1) symmetry is embedded in $M_2\times S_1$. We numerically construct different winding number vacua, the vortices interpolating between them, and simulate the collisions of these vortices. We show that classical transitions are generic at large boosts, independent of whether or not vortices miss each other in the compact $S_1$.