Upper bound of the charge diffusion constant in holography
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866909232605954048 |
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| author | Huh, Kyoung-Bum Jeong, Hyun-Sik Kim, Keun-Young Sun, Ya-Wen |
| author_facet | Huh, Kyoung-Bum Jeong, Hyun-Sik Kim, Keun-Young Sun, Ya-Wen |
| contents | 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 ($ω_{\text{eq}}, k_{\text{eq}}$) to the Einstein-Maxwell-Axion model. ($ω_{\text{eq}}, k_{\text{eq}}$) 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 $D = ω_{\text{eq}}/k_{\text{eq}}^2$. We show that the upper bound proposal also works for the charge diffusion and ($ω_{\text{eq}}, k_{\text{eq}}$), at low $T$, is determined by $D$ and the scaling dimension $Δ(0)$ of an infra-red operator as $(ω_{\text{eq}}, \, k_{\text{eq}}^2) \,=\, (2 πT Δ(0) \,, ω_{\text{eq}}/D)$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_07515 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Upper bound of the charge diffusion constant in holography Huh, Kyoung-Bum Jeong, Hyun-Sik Kim, Keun-Young Sun, Ya-Wen High Energy Physics - Theory 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 ($ω_{\text{eq}}, k_{\text{eq}}$) to the Einstein-Maxwell-Axion model. ($ω_{\text{eq}}, k_{\text{eq}}$) 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 $D = ω_{\text{eq}}/k_{\text{eq}}^2$. We show that the upper bound proposal also works for the charge diffusion and ($ω_{\text{eq}}, k_{\text{eq}}$), at low $T$, is determined by $D$ and the scaling dimension $Δ(0)$ of an infra-red operator as $(ω_{\text{eq}}, \, k_{\text{eq}}^2) \,=\, (2 πT Δ(0) \,, ω_{\text{eq}}/D)$, 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. |
| title | Upper bound of the charge diffusion constant in holography |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2111.07515 |