Diving inside holographic metals

• Published in: The journal of high energy physics Vol. 2025; no. 5; pp. 72 - 35
• Main Authors: Carballo, Javier, Patra, Ayan K., Pedraza, Juan F.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 08.05.2025; Springer Nature B.V; SpringerOpen
• Subjects: AdS-CFT Correspondence; Black Holes; Black Holes in String Theory; Charge density; Classical and Quantum Gravitation; Collapse; Condensed matter physics; Deformation effects; Electron clouds; Elementary Particles; Entanglement; Fermions; Field theory; Fixed points (mathematics); High energy physics; Holography; Holography and Condensed Matter Physics (AdS/CMT); Operators (mathematics); Phase transitions; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Singularities; String Theory; Wormholes; Black Holes in String Theory; AdS-CFT Correspondence; Holography and Condensed Matter Physics (AdS/CMT); Black Holes
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP05(2025)072

A bstract 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.