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<p>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-<i>p</i><sub><i>t</i></sub> 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 <i>a</i>-function, which decays with a specific power of <i>p</i><sub><i>t</i></sub> 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-<i>p</i><sub><i>t</i></sub>. 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.</p>

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Diving inside holographic metals

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月8日

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  • Javier Carballo,
  • Ayan K. Patra,
  • Juan F. Pedraza

摘要

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-pt 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 pt 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-pt. 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.