Friedel oscillations and horizon charge in 1D holographic liquids

TL;DR

The paper demonstrates that Friedel oscillations at wavevector 2kF emerge in a 1+1d holographic liquid once nonperturbative bulk monopole effects are included in a 3d Maxwell-AdS dual with a finite density. By dualizing the bulk gauge field to a scalar Theta and exploiting the compactness of the U(1) gauge group, monopole instantons acquire a Berry phase in the presence of a background density, yielding a distinctive oscillatory contribution to density correlators that aligns with Luttinger-count expectations when Dirac quantization is saturated. The analysis covers both high-temperature (probe) and zero-temperature (gravity-coupled) regimes, revealing a Lorentzian peak at k = ρ q_m at finite T and a power-law singularity at T = 0 controlled by a gravity-dressed sound mode. These results imply a Fermi-surface-like structure behind the horizon, offering a gauge-invariant signature of underlying fermionic behavior in a strongly coupled holographic setup and suggesting robust, generic mechanisms for momentum-space structure tied to horizon charge. The work also discusses UV completions, potential Chern-Simons extensions, and prospects for extending these ideas to higher dimensions.

Abstract

In many-body fermionic systems at finite density correlation functions of the density operator exhibit Friedel oscillations at a wavevector that is twice the Fermi momentum. We demonstrate the existence of such Friedel oscillations in a 3d gravity dual to a compressible finite-density state in a (1+1) dimensional field theory. The bulk dynamics is provided by a Maxwell U(1) gauge theory and all the charge is behind a bulk horizon. The bulk gauge theory is compact and so there exist magnetic monopole tunneling events. We compute the effect of these monopoles on holographic density-density correlation functions and demonstrate that they cause Friedel oscillations at a wavevector that directly counts the charge behind the bulk horizon. If the magnetic monopoles are taken to saturate the bulk Dirac quantization condition then the observed Fermi momentum exactly agrees with that predicted by Luttinger's theorem, suggesting some Fermi surface structure associated with the charged horizon. The mechanism is generic and will apply to any charged horizon in three dimensions. Along the way we clarify some aspects of the holographic interpretation of Maxwell electromagnetism in three bulk dimensions and show that perturbations about the charged BTZ black hole exhibit a hydrodynamic sound mode at low temperature.

Figures (5)

• Figure 1: Witten diagram used in calculation of contribution of monopole-anti-monopole pair to boundary theory density-density correlator. Solid wiggly lines indicate bulk-to-boundary correlators, and dotted gray lines indicate monopole-antimonopole interaction energy.
• Figure 2: Witten diagram illustrating one of four terms (the one we compute) in \ref{['wittenans']}.
• Figure 3: Different contributions to final answer \ref{['wittenans']}, corresponding to different ways to attach boundary points to the bulk monopole. We only compute $A$; $B$ is related to it by switching $y_1$ and $y_2$. $C$ and $D$ are not expected to contribute interesting correlations. $E$ is a disconnected diagram that can be seen in \ref{['bdycontm']}: it is essentially equivalent to the tree-level answer and will cancel if we compute a properly normalized two-point function.
• Figure 4: Monopole-antimonopole pair at large spatial separation and finite temperature. Field lines cannot spread out in $\tau$ (due to compactness) or in $r$ (due to AdS kinematics), making the problem essentially one dimensional.
• Figure 5: Numerical evaluation of monopole fugacity \ref{['fug1']} (solid line) compared with analytic expression \ref{['fug_anal']} (dotted line), with $\bar{r}_{\star} = 200$. As described above only the $r$-dependence can be computed within our framework, and thus an $r$-independent (and in fact IR-divergent) constant has been adjusted in the fit.