Entanglement Entropy and Complexity in Dyonic Quantum Black Holes

TL;DR

This work investigates holographic entanglement entropy and holographic complexity for three-dimensional dyonic quantum black holes in a double-holography (KR braneworld) setup, incorporating all-order quantum backreaction from bulk fields. It uses RT and island prescriptions to compute EE, revealing island phases when RT surfaces intersect the brane and showing EE saturation for both quantum black holes and quantum dressed defects. For HC, it analyzes both the perturbative CV and exact CA prescriptions, finding universal leading quantum corrections and a thermodynamic interpretation of late-time growth, with quantum dressed defects showing vanishing growth. The CA approach yields tractable all-orders results and highlights the role of thermodynamic variables in complexity dynamics, providing a coherent picture linking quantum backreaction, islands, and information-theoretic measures in holographic gravity. These insights pave the way for extensions to rotation, wedge holography, and first-law-like formulations of complexity in quantum-corrected spacetimes.

Abstract

In this work, we study the holographic entanglement entropy (HEE) and holographic complexity (HC) for three-dimensional dyonic quantum black holes, incorporating corrections arising from bulk quantum fields in the setup of double holography. We investigate the holographic entanglement entropy through the holographic Ryu-Takayanagi (RT) prescription and the island prescription. Using RT extremization, we evaluate HEE for connected and disconnected (island) surfaces and show islands emerge when RT surfaces intersect the brane; entanglement entropy grows with subregion size and ultimately saturates for quantum black holes as well as dressed defects. For complexity, we analyze both CV (perturbative) and CA (exact, all-orders) prescriptions: the leading quantum corrections feature universal behavior and the late-time growth can be expressed in thermodynamic variables, obeying generalized Lloyd-type bounds. In contrast, quantum dressed defects exhibit vanishing late-time growth. The CA prescription proves to be more tractable nonperturbatively and yields a thermodynamic interpretation of complexity growth.

Figures (13)

• Figure 1: This schematic diagram shows the RT surface in the Karch-Randall brane $\mathcal{B}$ at $x=0$ (thick blue line), enclosing a three-dimensional black hole (shaded blue region) with a thick black line representing the Poincaré disk of the $\text{AdS}_{4}$-C metric. Left: Connecting RT surface, Right: Disconnected surface intersecting brane at fixed $r_0$ (in shaded blue region) represent the region inside the black hole.
• Figure 2: Left:$A_{C}$ vs subregion radius $(x_{1}-\epsilon)$ for $\kappa=-1$, Right:$A_{C}$ vs subregion radius $(x_{1}-\epsilon)$ for $\kappa=1$.
• Figure 3: Left:$A_{D}$ vs $\alpha$ for $\kappa = -1$, $q=0$, Right:$A_{D}$ vs $\alpha$ for $\kappa =1$, $q=0$ and different value of $x_c$'s
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