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Gravity Dual of Quantum Information Metric

Masamichi Miyaji, Tokiro Numasawa, Noburo Shiba, Tadashi Takayanagi, Kento Watanabe

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 AdS spacetime when the perturbation is exactly marginal. We confirm our claim in several examples.

Gravity Dual of Quantum Information Metric

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 AdS spacetime when the perturbation is exactly marginal. We confirm our claim in several examples.

Paper Structure

This paper contains 58 equations, 2 figures.

Figures (2)

  • Figure 1: A time slice in the Penrose diagram of eternal AdS black hole which connects the two boundaries dual to the thermofield doubled CFTs.
  • Figure 2: We compare the finite part of our holographic result $\hbox{Vol}(\Sigma)/(R^{d+1}V_1)$ (blue) with that of our CFT result $2G_{\lambda\lambda}/V_1$ (red) as a function of the time $t$ for the TFD state. They deviates only slightly. We set $\beta=2\pi$.