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.
Highlights
Many quantum Hall systems can be described by Chern-Simons theories, where topological entanglement entropy can be computed; it equals the S00 component of the modular S-matrix of the theory [3]
In this paper we show that certain soft-wall models of confinement do support entangling surfaces with the disk topology and, a constant term in the entanglement entropy due to the Einstein-Hilbert part of the bulk action is absent
We show that it is possible to obtain nonvanishing topological entanglement entropy, γ, in holography
Summary
We briefly review the physical interpretation of the quantum dimension appearing in the Chern-Simons theory and its relation to the entanglement entropy. We finish the section by outlining how to obtain the relation between topological entanglement entropy and ground state degeneracy on Σg × S1. A simple way to find a nice expression for the limit we are interested is to use the level-rank duality i.e. the partition function of SU(N )k and SU(k)N on S3 are related by [19]. The Gauss-Bonnet theory is one of the simplest extensions of the Einstein gravity It is described by the Einstein-Hilbert action with a 4-dimensional Euler density, the GaussBonnet term, added. We show that contributions from the Gauss-Bonnet term to the ground state entropy and to the entanglement entropy are related by (1.3)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
