Quantum information metric of conical defect

Abstract

A concept of measuring the quantum distance between two different quantum states which is called quantum information metric is presented. The holographic principle (AdS/CFT) suggests that the quantum information metric G λλ between perturbed state and unperturbed state in field theory has a dual description in the classical gravity. In this work we calculate the quantum information metric of a theory which is dual to a conical defect geometry and we show that it is n times the one of its covering space. We also give a holographic check for our result in the gravity side. Meanwhile, it was argued that G λλ is dual to a codimensionone surface in spacetime and satisfies G λλ = n d ·Vol(Σ max )/L d . We show that the coefficient n d for conical defect should be rescaled by n 2 from the one for AdS. A limit case of conical defect -the massless BTZ black hole-is also considered. We show that the quantum information metric of the massless BTZ black hole disagrees with the one obtained by taking the vanishing temperature limit in BTZ black hole. This provides a new arena in differiating the different phases between BTZ spacetime and its massless cousin. *

Information geometry encoded in bulk geometry

“…It associates information geometry with dynamics of gravity. The information metric is related to a codimension-2 hypersurface in this paper, while it is related to a codimension-1 hypersurface in [7][8][9][10][11].…”

“…The geometrical quantity associated with the information metric is local in the bulk direction, while the minimal surface associated with entanglement entropy is not. Information metrics have been studied in the context of the AdS/CFT correspondence in [7][8][9][10][11][12][13][14][15].…”

“…They examined a gravity dual of a filed theory that is obtained by gluing the above two theories and found that the information metric is represented by the volume of a hypersurface that is the time slice in the bulk JHEP06(2020)107 wihich ends on the time slice on the boundary. Further developments in this derection have been made in [8][9][10][11]. A different type of information metric has been investigated in [13][14][15].…”

Holographic relations for OPE blocks in excited states

“…The N → ∞ limit of the CD metric and the M → 0 limit of the BTZ metric both produce the 0M metric, but the respective conjugacy classes (2.19) by which elements are identified are not related in this way. Some differences between these limits have been noted in [32]. For these reasons we treat the 0M solution as a distinct case throughout.…”

How information geometry is encoded in bulk geometry

“…This talk is based on [7]. Information metrics have been investigated in the context of the AdS/CFT correspondence in [8][9][10][11][12][13][14][15][16].…”