paper

Large-N transitions of the connectivity index

arXiv:1410.7773 · doi:10.1007/JHEP02(2015)083

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

39 pages, 4 figures; v2 a new section 8 has been added to emphasise aspects of separability in the IR effective theory and the relation with multi-gravity, references added; v3 a proper account of the IR effects of U(1) (singleton) degrees of freedom has been added with appropriate changes in sections 3, 4.3, 9, main conclusions unchanged, changes match published version

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