Large-N transitions of the connectivity index

Understand

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.