Bounds on charge and heat diffusivities in momentum dissipating holography

TL;DR

The paper investigates Planckian diffusion bounds in momentum-dissipating holographic models. It first analyzes a simple massive gravity setup and finds no lower bound for the thermo-electric diffusion constants $D_+$ and $D_-$, nor a robust linear-$T$ resistivity. By adding a dilaton and focusing on a critical $oldsymbol{ extmu=0}$ regime, it obtains $D_c^{( ext{crit})}=1/(2\pi T)$ and $D_h^{( ext{crit})}=2\pi T/|eta|$, yielding a bound on their sum: $D_h^{( ext{crit})}+D_c^{( ext{crit})}\ge 1/(2\pi T)$, which aligns with Kovtun/Hartnoll diffusion-bound proposals. This provides a concrete holographic example where a bound on the sum of thermo-electric diffusion constants arises, underscoring the role of dilaton physics and criticality in Planckian transport behavior.

Abstract

Inspired by a recently conjectured universal bound for thermo-electric diffusion constants in quantum critical, strongly coupled systems and relying on holographic analytical computations, we investigate the possibility of formulating Planckian bounds in different holographic models featuring momentum dissipation. For a simple massive gravity dilaton model at zero charge density we find robust linear in temperature resistivity and entropy density alongside a constant electric susceptibility. In addition we explicitly find that the sum of the thermo-electric diffusion constants is bounded.

Figures (1)

• Figure 1: Sample diagrams to illustrate the behavior of thermo-electric diffusion constants at (left) finite chemical potential, namely $\mu = 1$ (blue line for $D_-$ and green line for $D_+$), and (right) $\mu=0$ (blue line for $D_-=D_c$ and green line for $D_+=D_h$). The graviton mass parameter has been chosen to be $\beta = -1$.