Near-extremal holographic charge correlators
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arXiv
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| Format: | Preprint |
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2025
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| author | Goutéraux, Blaise Ramirez, David M. Sanchez-Garitaonandia, Mikel Supiot, Clément |
| author_facet | Goutéraux, Blaise Ramirez, David M. Sanchez-Garitaonandia, Mikel Supiot, Clément |
| contents | We analytically compute the low-temperature charge correlators in near-extremal black holes with a planar horizon and an infrared $\mathrm{AdS}_2\times \Bbb{R}^2$ extremal geometry, finding excellent agreement with numerical calculations. The analytical result consistently describes the crossover between the hydrodynamic diffusive regime at low frequencies and wavenumbers, and the quantum, zero-temperature regime at high frequencies and wavenumbers. We analytically resolve the successive collisions between the diffusive pole and the non-hydrodynamic poles sourced by the infrared $\mathrm{AdS}_2\times \Bbb{R}^2$ geometry. We demonstrate that in the $T=0$ limit, a pair of gapless poles survive with a dispersion relation $ω_\pm=-i d_2 k^2-i d_4 k^4-i\tilde d_4 k^4(\pm iπ+\log k^2) $. The nonanalytic contributions arise from the interplay with the branch cut formed by the condensation of the non-hydrodynamic poles. The real part is caused by the `snatching' of one of the non-hydrodynamic poles by the hydrodynamic diffusive pole. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_11974 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Near-extremal holographic charge correlators Goutéraux, Blaise Ramirez, David M. Sanchez-Garitaonandia, Mikel Supiot, Clément High Energy Physics - Theory Strongly Correlated Electrons We analytically compute the low-temperature charge correlators in near-extremal black holes with a planar horizon and an infrared $\mathrm{AdS}_2\times \Bbb{R}^2$ extremal geometry, finding excellent agreement with numerical calculations. The analytical result consistently describes the crossover between the hydrodynamic diffusive regime at low frequencies and wavenumbers, and the quantum, zero-temperature regime at high frequencies and wavenumbers. We analytically resolve the successive collisions between the diffusive pole and the non-hydrodynamic poles sourced by the infrared $\mathrm{AdS}_2\times \Bbb{R}^2$ geometry. We demonstrate that in the $T=0$ limit, a pair of gapless poles survive with a dispersion relation $ω_\pm=-i d_2 k^2-i d_4 k^4-i\tilde d_4 k^4(\pm iπ+\log k^2) $. The nonanalytic contributions arise from the interplay with the branch cut formed by the condensation of the non-hydrodynamic poles. The real part is caused by the `snatching' of one of the non-hydrodynamic poles by the hydrodynamic diffusive pole. |
| title | Near-extremal holographic charge correlators |
| topic | High Energy Physics - Theory Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2506.11974 |