Anyonic Excitations in Warped and Curved AdS Backgrounds

TL;DR

This paper investigates how geometric deformations like conical defects in warped and curved AdS$_3$ backgrounds influence anyonic excitations, fusion, and braiding properties within Chern-Simons theory, impacting holographic duals and topological features.

Contribution

It introduces a detailed analysis of the effects of curvature and geometric defects on anyonic excitations and their topological properties in warped AdS$_3$ backgrounds, combining analytical and numerical methods.

Findings

Curvature modifies fusion and braiding properties of anyons.

Geometric deformations influence the topological structure and holographic duals.

Deformations impact entanglement and quantum error correction in the models.

Abstract

This work studies anyonic excitations in warped and curved AdS$_3$ backgrounds via Chern-Simons theory. By incorporating geometric deformations such as conical defects, it is shown that curvature modifies the fusion and braiding properties through corrections to modular data in SU($N$)$_k$ models. Analytical models and numerical simulations reveal how these deformations affect the topological structure and influence holographic duals, especially in relation to entanglement and quantum error correction.