Diving inside holographic metals
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| author | Carballo, Javier Patra, Ayan K. Pedraza, Juan F. |
| author_facet | Carballo, Javier Patra, Ayan K. Pedraza, Juan F. |
| contents | We investigate the gravitational dual of a fermionic field theory at finite temperature and charge density in two spatial dimensions, subject to a deformation by a relevant scalar operator. This makes a $(3+1)$-dimensional Einstein-Maxwell system coupled to a free fermion fluid, known as an electron cloud, undergo a holographic renormalization group flow. The inner (Cauchy) horizon is destroyed and the near-singularity metric instead adopts the form of a positive-$p_t$ Kasner cosmology, signaling the collapse of the Einstein-Rosen bridge. Previous studies have suggested that this collapse hinders direct probing of the singularity. Nonetheless, we propose and compute several CFT observables that characterize the interior and near-singularity geometries. These include the thermal $a$-function, which decays with a specific power of $p_t$ as nearly all CFT degrees of freedom are integrated out, and two-point correlators for neutral and charged operators, with the latter directly probing the singularity despite the positive-$p_t$. We also calculate characteristic velocities related to entanglement and complexity growth in the time-evolved thermofield double state, as well as the butterfly effect indicative of operator spreading. Notably, the deformed electron cloud features a Lifshitz IR fixed point and an additional Kasner trans-IR fixed point, absent in neutral RG flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07748 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diving inside holographic metals Carballo, Javier Patra, Ayan K. Pedraza, Juan F. High Energy Physics - Theory General Relativity and Quantum Cosmology We investigate the gravitational dual of a fermionic field theory at finite temperature and charge density in two spatial dimensions, subject to a deformation by a relevant scalar operator. This makes a $(3+1)$-dimensional Einstein-Maxwell system coupled to a free fermion fluid, known as an electron cloud, undergo a holographic renormalization group flow. The inner (Cauchy) horizon is destroyed and the near-singularity metric instead adopts the form of a positive-$p_t$ Kasner cosmology, signaling the collapse of the Einstein-Rosen bridge. Previous studies have suggested that this collapse hinders direct probing of the singularity. Nonetheless, we propose and compute several CFT observables that characterize the interior and near-singularity geometries. These include the thermal $a$-function, which decays with a specific power of $p_t$ as nearly all CFT degrees of freedom are integrated out, and two-point correlators for neutral and charged operators, with the latter directly probing the singularity despite the positive-$p_t$. We also calculate characteristic velocities related to entanglement and complexity growth in the time-evolved thermofield double state, as well as the butterfly effect indicative of operator spreading. Notably, the deformed electron cloud features a Lifshitz IR fixed point and an additional Kasner trans-IR fixed point, absent in neutral RG flows. |
| title | Diving inside holographic metals |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2408.07748 |