Large-N transitions of the connectivity index

Aprile, Francesco; Niarchos, Vasilis

Abstract

The connectivity index, defined as the number of decoupled components of a separable quantum system, can change under deformations of the Hamiltonian or during the dynamical change of the system under renormalization group flow. Such changes signal a rearrangement of correlations of different degrees of freedom across spacetime and field theory space. In this paper we quantify such processes by studying the behavior of entanglement entropy in a specific example: the RG flow in the Coulomb branch of large-N superconformal field theories. We find evidence that the transition from the non-separable phase of the Higgsed gauge theory in the UV to the separable phase of deformed decoupled CFTs in the IR exhibits sharp features in the middle of the RG flow in the large-N limit. The entanglement entropy on a sphere with radius ℓ exhibits the formation of a separatrix on the co-dimension-two Ryu-Takayanagi surface in multi-centered brane geometries above a critical value of ℓ. We discuss how other measures of entanglement and separability based on the relative quantum entropy and quantum mutual information might detect such transitions between non-separable and separable phases and how they would help describe some of the key properties of the IR physics of such flows.

Citation

Aprile, F., & Niarchos, V. (2015). Large-N transitions of the connectivity index. Journal of High Energy Physics, 2015(2), Article 083. https://doi.org/10.1007/jhep02%282015%29083

• Journal Article Type: Article
• Acceptance Date: Jan 6, 2015
• Online Publication Date: Feb 12, 2015
• Publication Date: Feb 12, 2015
• Deposit Date: Oct 15, 2016
• Publicly Available Date: Feb 3, 2017
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2015
• Issue: 2
• Article Number: 083
• DOI: https://doi.org/10.1007/jhep02%282015%29083
• Public URL: https://durham-repository.worktribe.com/output/1395371