Abstract
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 derivative 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.
Highlights
Using the holographic correspondence as a tool, we study the dynamics of first-order phase transitions in strongly coupled gauge theories at finite temperature
For a scalar field Φ in 3+1 dimensions, with potential having an absolute minimum at Φt and a local minimum at Φf, the bounce action is defined by SB = SE(ΦB) − SE(Φf ), where SE is the Euclidean action for the scalar field and ΦB is called “the bounce”
We have studied the dynamics of first-order phase transitions in strongly coupled planar gauge theories
Summary
As a warm-up, we revisit the analysis performed in [8] of the compact Randall-Sundrum (RS) model with two relevant scales, given by the temperature T and the radial distance between a Standard-Model brane (the TeV brane) and a Planck brane. The horizon radius of the AdS black hole and the radion are promoted to space-dependent fields whose effective action, describing the bounce, is estimated. Where F is the free energy, V3 = d3x is the infinite flat 3d space volume and Sren is the renormalized on-shell Euclidean action The latter, as reviewed in [8], can be obtained as the difference between the on-shell value of the action (2.1) on the black hole solution (2.2). 4π T p dρ ρ2 6π2(∂ρTh)2 + 2π4(3Th4 − 4Th3T ) This formula is the main result of this section: our analysis determines the relative coefficient between the derivative and the potential term in the effective action for the “temperature field” Th(ρ), for the entire class of strongly coupled planar (3+1)-dimensional CFT with an AdS5 black hole holographic dual.
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