Large-N transitions of the connectivity index

TL;DR

This paper investigates how the connectivity index, related to the number of decoupled components in a quantum system, changes during RG flows in large-N superconformal field theories, revealing sharp phase transitions in entanglement structure.

Contribution

It provides a quantitative analysis of entanglement entropy behavior during RG flows, identifying sharp phase transitions in the connectivity index in large-N theories.

Findings

Evidence of sharp phase transitions in entanglement entropy during RG flow.

Formation of a separatrix on the Ryu-Takayanagi surface at a critical scale.

Potential for other entanglement measures to detect phase transitions.

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 $\ell$ exhibits the formation of a separatrix on the co-dimension-two Ryu-Takayanagi surface in multi-centered brane geometries above a critical value of $\ell$. 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.