Towards strange metallic holography

TL;DR

This work develops a holographic framework for strange metal phenomenology by coupling a neutral Lifshitz quantum critical bath (z determining scaling) to a finite density of gapped probe charge carriers described by flavor D-branes. Through DBI dynamics and holographic RG analysis, it derives DC, Hall, and AC conductivities, revealing nontrivial $T$- and $\omega$-scaling and showing how linear resistivity can emerge for suitable $z$, notably $z=2$, in a controlled setting. It also maps the thermodynamics and transport to the Lifshitz fixed points, identifying UV divergences and boundary conditions, and explores how massive carriers and backreaction modify the transport, including Drude-like peaks and power-law tails. The paper outlines several top-down realizations of Lifshitz geometries from string theory (F-theory, brane polarization, and Fermi-gas backreaction), and discusses a landscape of Lifshitz superconductors and model-building directions to tune exponents and Hall phenomena. Overall, it provides a concrete, controllable holographic path to model non-Fermi-liquid transport and outlines future extensions to broader anomalous observables and condensed-matter phenomenology.

Abstract

We initiate a holographic model building approach to `strange metallic' phenomenology. Our model couples a neutral Lifshitz-invariant quantum critical theory, dual to a bulk gravitational background, to a finite density of gapped probe charge carriers, dually described by D-branes. In the physical regime of temperature much lower than the charge density and gap, we exhibit anomalous scalings of the temperature and frequency dependent conductivity. Choosing the dynamical critical exponent $z$ appropriately we can match the non-Fermi liquid scalings, such as linear resistivity, observed in strange metal regimes. As part of our investigation we outline three distinct string theory realizations of Lifshitz geometries: from F theory, from polarised branes, and from a gravitating charged Fermi gas. We also identify general features of renormalisation group flow in Lifshitz theories, such as the appearance of relevant charge-charge interactions when $z \geq 2$. We outline a program to extend this model building approach to other anomalous observables of interest such as the Hall conductivity.

Figures (5)

• Figure 1: Our model will describe probe charge carriers interacting with a quantum critical Lifshitz bath. Parameters include the dynamical scaling exponent $z$, the energy gap $E_\text{gap}$ and density $J^t$ of the carriers. Ultimately the charge-charge interactions are mediated by the Lifshitz sector.
• Figure 2: The real part of the conductivity as a function of frequency for $z=1$ (left) and $z=2$ (right). The four curves in each graph correspond to $\frac{1}{\tau_\text{eff.} 2\pi \alpha' L^2} \frac{J^t}{T^{2/z}}$ equal to $\{0,10,20,30\}$ (left) and $\{0,2,5,10\}$ (right), with $J^t=0$ giving the expected constant lines.
• Figure 3: Schematic depiction of the massive flavor brane in the string regime (left) and spike regime (right).
• Figure 4: The brane profile for $z=1$ (left) and $z=2$ (right) with $\frac{1}{\tau_\text{eff.} 2\pi \alpha' L^2} \frac{J^t}{T^{2/z}}$ equal to $\{10,100,1000,10000\}$ and $\{0.5,10,500,10000\}$ respectively. In all plots $\frac{m}{T} = 20$ and $n=2$.
• Figure 5: The dissipative conductivity for $z=1$ (left) and $z=2$ (right), with the same parameter values as in figure \ref{['fig:t1t2plot']}