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arXiv · 2408.07748

Diving inside holographic metals

Javier Carballo·Ayan K. Patra·Juan F. Pedraza
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Abstract

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.

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Javier Carballo, Ayan K. Patra, Juan F. Pedraza. 2024-08-14. Diving inside holographic metals. https://doi.org/10.1007/jhep05(2025)072

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