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arXiv · 1902.08669

A Non-Equilibrium Approach To Holographic Superconductors Using Gradient Flow

Paul Mikula·Margaret E. Carrington·Gabor Kunstatter
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Abstract

We study a charged scalar field in a bulk 3+1 dimensional anti-deSitter spacetime with a planar black hole background metric. Through the AdS/CFT correspondence this is equivalent to a strongly coupled field theory in 2+1 dimensions describing a superconductor. We use the gradient flow method and solve the flow equations numerically between two fixed points: a vacuum solution and a hairy black hole solution. We study the corresponding flow on the boundary between a normal metal phase and a superconducting phase. We show how the gradient flow moves fields between two fixed points in a way that minimizes the free energy of the system. At the fixed points of the flow the AdS/CFT correspondence provides an equivalence between the Euclidean on-shell action in the bulk and the free energy of the boundary, but it does not tell us about fields away from equilibrium. However, we can formally link static off-shell configurations in the bulk and in the boundary at the same point along the flow. For quasi-static evolution at least, it may be reasonable to think of this link as an extension of the AdS/CFT correspondance.

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Paul Mikula, Margaret E. Carrington, Gabor Kunstatter. 2019-07-10. A Non-Equilibrium Approach To Holographic Superconductors Using Gradient Flow. https://doi.org/10.1103/physrevd.100.046004

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