Testing the effective action approach to bubble nucleation in holography

TL;DR

This paper evaluates the effective action approach to bubble nucleation in holography by comparing it with full gravitational solutions, demonstrating good agreement and simplifying the computational process.

Contribution

It tests the effectiveness of the derivative expansion of the holographic effective action for bubble nucleation against full gravitational solutions.

Findings

Good agreement between effective action and full gravitational solutions.

Simplifies bubble nucleation computations in holography.

Validates the derivative expansion approach for critical bubbles.

Abstract

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.