Quantum critical charge response from higher derivatives: is more different?

TL;DR

This work analyzes quantum critical charge transport in 2+1D CFTs through holography with an expansive family of higher-derivative bulk terms. By encoding HD couplings in a diagonal X-matrix built from the Weyl tensor, the authors derive a rich set of conductivity behaviors, including unbounded $\sigma$, diffusion $D$, and susceptibility $\chi$, as well as an infinite self-dual line where $\sigma(w)$ is frequency-independent. They show that S-duality maps finite HD theories to infinite-series duals, and they establish sum rules and stability across the explored parameter space. The results are connected to O($N$) CFTs via Drude-like peaks and QMC data, highlighting particle-like transport at quantum critical points and the robustness of holographic predictions against HD corrections. Overall, the paper significantly broadens the landscape of holographic charge response in quantum critical regimes and clarifies the role of dualities and higher-curvature terms in transport phenomena.

Abstract

We present new possibilities for the charge response in the quantum critical regime in 2+1D using holography, and compare them with field theory and recent quantum Monte Carlo results. We show that a family of (infinitely many) higher derivative terms in the gravitational bulk leads to behavior far richer than what was previously obtained. For example, we prove that the conductivity becomes unbounded, undermining previously obtained constraints. We further find a non-trivial and infinite set of theories that have a self-dual conductivity. Particle-vortex or S duality plays a key role; notably, it maps theories with a finite number of bulk terms to ones with an infinite number. Many properties such as sum rules and stability conditions are proved.

Figures (11)

• Figure 1: a) Sketch of the subspace of holographic theories describing the charge response of CFTs in 2+1D. It encompasses any action with $n_{\rm term}$ terms containing 2 field strengths coupled to curvature tensors. The arrows indicate S-duality. The central regions (red) have a self-dual, $\omega$-independent conductivity $\sigma$. The star corresponds to the R-charge response of superconformal Yang-Mills. b) New allowed asymptotics for the d.c. conductivity, diffusion constant and susceptibility; $\gamma_1$ parameterizes a 6-derivative term.
• Figure 2: Real part of the conductivity for $\gamma=0$, with the corresponding $(\gamma_1,\gamma_2)$ indicated in the inset. Inset: portion of the allowed parameter space for $\gamma=0$, and contour plot of $\sigma(0)$, where blue/red indicates small/large values. The green dashed lines in the main figure and inset are associated with the self-dual conductivity.
• Figure 3: Comparing the conductivity of (a) the quantum critical O($N\rightarrow\infty$) model to that of (b) the 6-derivative holographic action with $(\gamma,\gamma_1,\gamma_2)=(0,-1,0)$. The inverse conductivities (dashed) also show similarities. Insets: analytic structure of $\sigma(w)$ in complex $w$-plane: crosses/circles represent poles/zeros (the line in (a) is a branch cut).
• Figure 4: a) The markers correspond to the imaginary-frequency conductivity obtained from large-scale quantum Monte Carlo simulations on the O(2) QCPads-qmc. The blue (dot-dashed) and red (solid) curves are the fits to the data using the Weyl actionads-qmc or the one including 6-derivative terms in addition, respectively. The values of the fitting parameters are shown. b) Corresponding real-frequency behavior.
• Figure 5: Comparison between the exact S-dual conductivity $\hat{\sigma}=1/\sigma$ of the Weyl action at $\gamma=1/12$, and the one obtained from truncating the infinite S-dual action to terms with at most $n=1,3,6$ powers of the Weyl tensor, $\hat{\sigma}_n$. $|z|$ denotes the complex norm.