Testing the effective action approach to bubble nucleation in holography

The nucleation of bubbles during a first-order phase transition has recently been explored using holographic duality, which can provide an important complement to standard perturbative methods. These computations typically require finding static and spatially inhomogeneous saddle points, known as critical bubbles, which correspond in the gravitational dual to solutions of nonlinear partial differential equations. A computationally simpler alternative is to use the gravitational dual to derive the effective action of the boundary theory in a derivative expansion, and then solve the resulting lower-dimensional equations of motion. Once the effective action, typically truncated at two derivatives, is obtained, the holographic theory can be set aside, and bubble solutions can be found from ordinary differential equations. In this paper, we test this approach in a simple holographic setup: a probe scalar field in a black brane background with nonlinear multi-trace boundary conditions. We compute critical bubble solutions both from the effective action and by solving the full gravitational equations, and find good agreement between the two methods.