Quantum information metric of conical defect

A concept of measuring the quantum distance between two different quantum states that is called quantum information metric has been presented. The holographic principle (anti-de Sitter/conformal field theory) suggests that the quantum information metric G(lambda lambda) 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 that 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(lambda lambda) is dual to a codimension-one surface in spacetime and satisfies G(lambda lambda) = n(d) . Vol(Sigma(max))/L-d. We show that the coefficient nd for conical defect should be rescaled by n(2) from the one for anti-de Sitter space. A limit case of conical defect-the massless Banados-Teitelboim-Zannelli (BTZ) black hole-is also considered. We show that the quantum information metric of a 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 differentiating the different phases between BTZ spacetime and its massless cousin.