AdS/CFT Duality and Anyons in $SU(N)_k$ Chern-Simons Theory

TL;DR

This paper explores the holographic duality of anyons in higher-rank SU(N)_k Chern-Simons theories, linking bulk topological features to boundary conformal field theories and proposing a modular tensor category structure.

Contribution

It extends the AdS/CFT correspondence to include higher-rank SU(N) Chern-Simons theories and establishes a connection between bulk Wilson loops and boundary defect operators.

Findings

Bulk-boundary correspondence for Wilson loops and defect operators

Analysis of fusion, braiding, and quantum dimensions of anyons

Proposal that boundary operator algebra forms a modular tensor category

Abstract

This paper investigates the holographic realization of anyons in \(SU(N)_k\) Chern-Simons theory within the AdS/CFT framework. The study extends traditional models, such as \(SU(2)\), to higher-rank groups like \(SU(3)\) and \(SU(4)\), focusing on the fusion, braiding, and quantum dimensions of anyons. A correspondence between Wilson loops in the bulk and boundary defect operators is established, demonstrating how the modular data of Chern-Simons theory relates to the boundary conformal field theory (CFT). The topological defects, fusion algebras, and operator spectra are analyzed from both the bulk and boundary perspectives, highlighting the relationship between bulk topological defects and boundary operators. Additionally, a conjecture is made that the boundary operator algebra forms a modular tensor category, providing a framework for exploring holographic dualities in topologically non-trivial systems.