Topological Entanglement Entropy, Ground State Degeneracy and Holography

TL;DR

This paper explores the relationship between topological entanglement entropy and ground state degeneracy in holographic models, highlighting the role of the topological Gauss-Bonnet term in the dual gravitational description.

Contribution

It introduces a holographic framework where topological entanglement entropy and ground state degeneracy are linked through the Gauss-Bonnet term, extending understanding of topological order in holography.

Findings

Topological entanglement entropy is non-zero due to the Gauss-Bonnet term.

Ground state degeneracy correlates with topological entanglement entropy in the models.

Finite correlation length achieved with a soft wall holographic model.

Abstract

Topological entanglement entropy, a measure of the long-ranged entanglement, is related to the degeneracy of the ground state on a higher genus surface. The exact relation depends on the details of the topological theory. We consider a class of holographic models where such relation might be similar to the one exhibited by Chern-Simons theory in a certain large N limit. Both the non-vanishing topological entanglement entropy and the ground state degeneracy in these holographic models are consequences of the topological Gauss-Bonnet term in the dual gravitational description. A soft wall holographic model of confinement is used to generate finite correlation length but keep the disk topology of the entangling surface in the bulk, necessary for nonvanishing topological entanglement entropy.