Abstract
We study the entanglement entropy in confining theories with gravity duals using the holographic prescription of Ryu and Takayanagi. The entanglement entropy between a region and its complement is proportional to the minimal area of a bulk hypersurface ending on their border. We consider a disk in 2+1 dimensions and a ball in 3+1 dimensions and find in both cases two types of bulk hypersurfaces with different topology, similar to the case of the slab geometry considered by Klebanov, Kutasov and Murugan. Depending on the value of the radius, one or the other type of hypersurfaces dominates the calculation of entanglement entropy. In 2+1 dimensions a useful measure of topological order of the ground state is the topological entanglement entropy, which is defined to be the constant term in the entanglement entropy of a disk in the limit of large radius. We compute this quantity and find that it vanishes for confining gauge theory, in accord with our expectations. In 3+1 dimensions the analogous quantity is shown to be generically nonzero and cutoff-dependent.
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.
