title: Distance between Quantum States and Gauge-Gravity Duality.
abstract: We study a quantum information metric (or fidelity susceptibility) in conformal field theories with respect to a small perturbation by a primary operator. We argue that its gravity dual is approximately given by a volume of maximal time slice in an anti-de Sitter spacetime when the perturbation is exactly marginal. We confirm our claim in several examples.
authors.affiliation: Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan.
authors.forename: Masamichi
authors.initials: M
authors.lastname: Miyaji
authors.affiliation: Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan.
authors.forename: Tokiro
authors.initials: T
authors.lastname: Numasawa
authors.affiliation: Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan.
authors.forename: Noburo
authors.initials: N
authors.lastname: Shiba
authors.affiliation: Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan.|Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa, Chiba 277-8582, Japan.
authors.forename: Tadashi
authors.initials: T
authors.lastname: Takayanagi
authors.affiliation: Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan.
authors.forename: Kento
authors.initials: K
authors.lastname: Watanabe