Using the holographic correspondence as a tool, we study the dynamics of first-order phase transitions in strongly coupled gauge theories at finite temperature. Considering an evolution from the large to the small temperature phase, we compute the nucleation rate of bubbles of true vacuum in the metastable phase. For this purpose, we find the relevant configurations (bounces) interpolating between the vacua and we compute the related effective actions. We start by revisiting the compact Randall-Sundrum model at high temperature. Using holographic renormalization, we compute the kinetic term in the effective bounce action, that was missing in the literature. Then, we address the full problem within the top-down Witten-Sakai-Sugimoto model. It displays both a confinement/deconfinement and a chiral symmetry breaking/restoration phase transition which, depending on the model parameters, can happen at different critical temperatures. For the confinement/deconfinement case we perform the numerical analysis of an effective description of the transition and also provide analytic expressions using thick and thin wall approximations. For the chiral symmetry transition, we implement a variational approach that allows us to address the challenging non-linear problem stemming from the Dirac-Born-Infeld action.
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