Thin walls and junctions: Vacuum decay in multidimensional field landscapes

We study tunneling between vacua in multidimensional field spaces in the thin wall approximation. The thin wall action generically gives rise to two types of saddle points. The first type corresponds to the well-known spherical instantons, but when the field space is multidimensional we find that it is necessary to include codimension two junctions to regulate and compute the fluctuation determinant and the tunneling rate. The second type of saddle point is novel and is present only when the field space is more than one dimensional. These saddle points have two or more negative modes, which confirms that in the presence of additional field directions spherical instantons continue to dominate vacuum decay. We identify regimes in parameter space in which additional field directions may quench certain channels of vacuum decay.