Luttinger's theorem, superfluid vortices, and holography

TL;DR

The paper addresses how finite-density holographic theories distinguish charge carried behind a horizon from charge outside the horizon. It derives a modified Luttinger relation for bulk fermions, $\frac{q}{(2\pi)^{d-1}}\sum_i V_i = \rho - \mathcal{A}$, where $\mathcal{A}$ is the horizon electric flux, and shows that a parallel deficit governs the Magnus force in holographic superfluids, $F_T^i = \epsilon^{ij}\frac{2\pi}{q}(\rho - \mathcal{A})v_j$. Across confining geometries, electron stars, RN-AdS, and dilatonic systems, the results tie observable boundary data to horizon (deconfined) degrees of freedom, offering a field-theoretical probe of fractionalization in strongly coupled gauge-gravity duals. The work connects Berry phases and transverse forces to horizon flux via bulk Gauss's law and discusses finite-temperature extensions and zero-temperature caveats. Overall, it provides a unified holographic framework to quantify how much charge is truly deconfined in finite-density quantum matter and how this deconfined sector alters key observables in both fermionic and bosonic contexts.

Abstract

Strongly coupled field theories with gravity duals can be placed at finite density in two ways: electric field flux emanating from behind a horizon, or bulk charged fields outside of the horizon that explicitly source the density. We discuss field-theoretical observables that are sensitive to this distinction. If the charged fields are fermionic, we discuss a modified Luttinger's theorem that holds for holographic systems, in which the sum of boundary theory Fermi surfaces counts only the charge outside of the horizon. If the charged fields are bosonic, we show that the the resulting superfluid phase may be characterized by the coefficient of the transverse Magnus force on a moving superfluid vortex, which again is sensitive only to the charge outside of the horizon. For holographic systems these observables provide a field-theoretical way to distinguish how much charge is held by a dual horizon, but they may be useful in more general contexts as measures of deconfined (i.e. "fractionalized") charge degrees of freedom.

Figures (8)

• Figure 1: Different ways to create a finite $U(1)$ density in a field theory with a holographic description. Left: The electric field at infinity is sourced by a horizon. Right: The electric field is sourced by charged fields in the bulk.
• Figure 2: Feynman diagram representing one-loop fermion density.
• Figure 3: Contour manipulations used in evaluation of \ref{['int1']}. Squiggles indicate non-analyticities in ${\lambda}(\omega)$ on real axis.
• Figure 4: Moving vortex slowly in a closed loop. The Berry phase counts the bulk charge enclosed by the loop in the bulk.
• Figure 5: Sending ripples down vortex string to compute Magnus force in linear response.