Vortices in holographic superfluids and superconductors as conformal defects

TL;DR

This work analyzes vortices in holographic superconductors and superfluids, revealing that low-energy vortex physics is governed by a conformal defect in an emergent IR CFT with an AdS$_2$-like horizon structure. The authors construct a UV-complete finite-temperature geometry describing a single vortex, and show that IR defect data control observable forces via defect-CFT Kubo formulas, while the full solution yields phase-dependent horizon properties, boundary observables, and vortex stability (Type I/II) governed by the bulk scalar charge. A novel horizon feature emerges: a finite-entropy RN–AdS bubble inside the vortex horizon, which saturates to the IR impurity entropy as $T\to0$. The paper also derives a defect-based framework for forces on moving vortices and discusses broader implications for holographic impurities, potential vortex lattices, and dual insulating phases via S-duality.

Abstract

We present a detailed study of a single vortex in a holographic symmetry breaking phase. At low energies the system flows to an nontrivial conformal fixed point. Novel vortex physics arises from the interaction of these gapless degrees of freedom with the vortex: at low energies the vortex may be understood as a conformal defect in this low energy theory. Defect conformal symmetry allows the construction of a simple infrared geometry describing a new kind of extremal horizon: a Poincare horizon with a small bubble of magnetic Reissner-Nordstrom horizon inside it that carries a single unit of magnetic flux and a finite amount of entropy even at zero temperature. We also construct the full geometry describing the vortex at finite temperature in a UV complete theory. We study both superfluid and superconducting boundary conditions and calculate thermodynamic properties of the vortex. A study of vortex stability reveals that the dual superconductor can be Type I or Type II, depending on the charge of the condensed scalar. Finally, we study forces on a moving vortex at finite temperature from the point of view of defect conformal symmetry and show that these forces can be expressed in terms of Kubo formulas of defect CFT operators.

Figures (20)

• Figure 1: Two different possibilities for infrared behavior of a holographic vortex. Left, vortex extends into horizon (dotted line) and never decouples. Right, vortex line terminated in bulk by magnetic monopole.
• Figure 2: Choice for the potential (\ref{['eq:potential']}), with $\mu^2 L^2 = -2$ and $V_0=-L^{-2}$.
• Figure 3: Scalar field $|\Phi|$ ( left panel) and gauge field $A_{\varphi}$ ( right panel) as a function of $\tilde{y}$ for $q L = 2, n = 1$. The core of the vortex is at $\tilde{y} = 1$, where both functions must vanish by regularity. At $\tilde{y} \to 0$ we approach the homogeneous ground state, and the scalar approaches the minimum of its potential.
• Figure 4: The scalar curvature of the $T=0$ horizon as a function of proper distance from the vortex core. The large positive peak near the core denotes a "bubble of Reissner-Nordström horizon" sticking out of the usual Poincaré horizon.
• Figure 5: Full entropy difference (defined later in \ref{['eq:difentropy']}) as a function of $T/(-\kappa)$ for $q\,L =2$. Squares correspond to $n=1$ and diamonds to $n=2$. The red triangle represents the impurity entropy (defined in \ref{['impSdef']}) extracted from the scaling solution \ref{['eq:ansatznear']}.