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Upper bound of the charge diffusion constant in holography
- Source :
- J. High Energ. Phys. 2022, 13 (2022)
- Publication Year :
- 2021
-
Abstract
- We investigate the upper bound of charge diffusion constant in holography. For this purpose, we apply the conjectured upper bound proposal related to the equilibration scales ($\omega_{\text{eq}}, k_{\text{eq}}$) to the Einstein-Maxwell-Axion model. ($\omega_{\text{eq}}, k_{\text{eq}}$) is defined as the collision point between the diffusive hydrodynamic mode and the first non-hydrodynamic mode, giving rise to the upper bound of the diffusion constant $D$ at low temperature $T$ as $D = \omega_{\text{eq}}/k_{\text{eq}}^2$. We show that the upper bound proposal also works for the charge diffusion and ($\omega_{\text{eq}}, k_{\text{eq}}$), at low $T$, is determined by $D$ and the scaling dimension $\Delta(0)$ of an infra-red operator as $(\omega_{\text{eq}}, \, k_{\text{eq}}^2) \,=\, (2 \pi T \Delta(0) \,, \omega_{\text{eq}}/D)$, as for other diffusion constants. However, for the charge diffusion, we find that the collision occurs at real $k_{\text{eq}}$, while it is complex for other diffusions. In order to examine the universality of the conjectured upper bound, we also introduce a higher derivative coupling to the Einstein-Maxwell-Axion model. This coupling is particularly interesting since it leads to the violation of the \textit{lower} bound of the charge diffusion constant so the correction may also have effects on the \textit{upper} bound of the charge diffusion. We find that the higher derivative coupling does not affect the upper bound so that the conjectured upper bound would not be easily violated.<br />Comment: v1: 23 pages, 10 figures; v2: minor edits, references added
- Subjects :
- High Energy Physics - Theory
Subjects
Details
- Database :
- arXiv
- Journal :
- J. High Energ. Phys. 2022, 13 (2022)
- Publication Type :
- Report
- Accession number :
- edsarx.2111.07515
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/JHEP07(2022)013