Metallic transports from Taub-NUT AdS black holes

TL;DR

The paper analyzes holographic DC transport in Taub-NUT AdS$_4$ black holes by employing a probe D-brane with a small external field to source massless U(1) carriers. It reveals a two-component conductivity $σ = \sqrt{σ_{U(1)}^2+σ_{thermal}^2}$, with $σ_{U(1)}$ from explicit carriers and $σ_{thermal}$ from thermally produced pairs; both components are strongly enhanced by frame dragging near the Misner string at low $T$, while frame-dragging effects are suppressed at high $T$ and $σ_{thermal}$ dominates. The analysis shows explicit scaling near the Misner string and a crossover to a thermal, $n$-independent regime for $T\gg T_{min}$, linking holographic metallic behavior to the geometry of Misner strings. These results illuminate how NUT charge and frame dragging shape boundary transport, providing a foundation for future studies of Hall response and entanglement in Taub-NUT AdS backgrounds.

Abstract

We compute holographic DC conductivity associated with the Taub-NUT-$AdS_4$ black holes following the probe D-brane approach. In particular, we examine the effects of frame dragging on charge transport in both low and high temperature regimes. Our analysis reveals that in the low temperature regime, the conductivity is sensitive to the presence of the Misner string that causes frame dragging. Notably, the increase in the conductivity near the Misner string is sharper as compared to points farther away from it. On the other hand, in the high temperature regime, the effects due to frame dragging are significantly suppressed, and the thermal contribution to the charge transport takes over that due to the U(1) charge carriers.

Figures (7)

• Figure 1: Position of the Misner string for different values of $\beta$. Here, BH denotes the black hole and MS denotes Misner's string.
• Figure 2: Conductivity vs temperature plot for $J_t=10$, $E=0.1$ and $T_{min}=0.29$.
• Figure 3: Conductivity vs temperature plot for $\beta=0$, $E=0.1$ and $J_t=10$
• Figure 4: Conductivity vs temperature plot for $\beta=-1$, $E=0.1$ and $J_t=10$
• Figure 5: Conductivity vs temperature plot for $\beta=1$. For points near the Misner string ($nM$), we set $\theta=0.1\pi$, and for points away from the Misner string ($fM$), we set $\theta=0.9\pi$. Here, we set $n=0.2$, $E=0.1$ and $J_t=10$.