Holographic charged Rényi entropies

Abstract

We construct a new class of entanglement measures by extending the usual definition of Rényi entropy to include a chemical potential. These charged Rényi entropies measure the degree of entanglement in different charge sectors of the theory and are given by Euclidean path integrals with the insertion of a Wilson line encircling the entangling surface. We compute these entropies for a spherical entangling surface in CFT's with holographic duals, where they are related to entropies of charged black holes with hyperbolic horizons. We also compute charged Rényi entropies in free field theories.ArXiv ePrint: 1310.4180 arXiv:1310.4180v2 [hep-th] An interesting exercise to gain better intuition for this background gauge field (2.15) is to expand the coordinates near the spherical entangling surface: t E = ρ sin θ and r = R + ρ cos θ with ρ R. To leading order in ρ/R, one then finds that the potential reduces to B µ E 2π dθ.

Twist operators in higher dimensions

“…However, we must remind the reader that for the free conformally coupled scalar in d ≥ 3, the heat kernel calculations in appendix B produced a result for h n,2 which was not in agreement with eq. (3.26), i.e., our 22 We note that this expansion was recently extended to include a chemical potential in discussing a new class of 'charged' Rényi entropies [51].…”

Entanglement negativity after a local quantum quench in conformal field theories

“…• Dynamical charged entanglement negativity Most recently, the concept of the charged Renyi entropies was proposed and studied in several works [47,48]. In particular, in Ref.…”

Entanglement entropy with background gauge fields

“…See also [5]. Sometimes, it is easier to compute the Rényi entropy [6][7][8], that is also physically relevant. While the holographic approaches for computing the entropies [9][10][11][12][13][14] provide valuable results, they are limited to the strongly coupled regime of the field theories.…”