Abstract
We study gauge and gravity backreaction in a holographic model of quantum quench across a superfluid critical transition. The model involves a complex scalar field coupled to a gauge and gravity field in the bulk. In earlier work (arXiv:1211.1776) the scalar field had a strong self-coupling, in which case the backreaction on both the metric and the gauge field can be ignored. In this approximation, it was shown that when a time dependent source for the order parameter drives the system across the critical point at a rate slow compared to the initial gap, the dynamics in the critical region is dominated by a zero mode of the bulk scalar, leading to a Kibble-Zurek type scaling function. We show that this mechanism for emergence of scaling behavior continues to hold without any self-coupling in the presence of backreaction of gauge field and gravity. Even though there are no zero modes for the metric and the gauge field, the scalar dynamics induces adiabaticity breakdown leading to scaling. This yields scaling behavior for the time dependence of the charge density and energy momentum tensor.
Highlights
Critical behavior there is really no well understood conceptual framework like the renormalization group which explains why all other scales decouple from the problem
We study gauge and gravity backreaction in a holographic model of quantum quench across a superfluid critical transition
It was shown that when a time dependent source for the order parameter drives the system across the critical point at a rate slow compared to the initial gap, the dynamics in the critical region is dominated by a zero mode of the bulk scalar, leading to a Kibble-Zurek type scaling function
Summary
Where Φ is a complex scalar field with charge q and Aμ is an abelian gauge field, and the other notations are standard. One of the spatial directions, which we will denote by θ will be considered to be compact. The radial direction will be denoted by r. The mass of the scalar is chosen in the range m2BF < m2 < m2BF + 1, where m2BF = −(d + 1)2/2 is the Breitenholer-Freedman bound. The boundary theory has a finite chemical potential μ, so that (2.2). Let us first set Φ = 0 (which is always a solution). As shown in [32], there is a value of the chemical potential μ = μ0 such that for μ < μ0 the preferred solution to Einstein equation is an AdS soliton ds.
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