Braid Group Representations and Defect Operators in AdS/CFT Correspondence

TL;DR

This paper explores the relationship between braid group representations, defect operators, and holography in the AdS/CFT correspondence, providing a unified framework for understanding topological defects and their boundary duals.

Contribution

It introduces a novel framework linking bulk braid representations with boundary defect operators within the AdS/CFT context, bridging topological quantum field theories and holography.

Findings

Braid group representations correspond to boundary defect operators.

Fusion and braiding operations are characterized in the holographic setting.

The work opens new research directions in holographic anyons and topological defects.

Abstract

This paper investigates the connection between braid group representations, defect operators, and holography within the AdS/CFT framework. It focuses on the correspondence between bulk Wilson loops and boundary defect operators, emphasizing how braid group representations map to these operators. The study also explores fusion and braiding operations in modular tensor categories, which are crucial for understanding anyons in topological quantum field theories. By providing a unified framework, this work bridges the gap between bulk and boundary physics and offers insights into the holographic realization of topological defects. The results suggest new avenues for research in holographic anyons and their applications in quantum field theory and condensed matter physics.