Emergence of Kinematic Space from Quantum Modular Geometric Tensor
arXiv:2110.08703 · doi:10.1016/j.physletb.2022.136893
Abstract
We generalize the Quantum Geometric Tensor by replacing a Hamiltonian with a modular Hamiltonian. The symmetric part of the Quantum Geometric Tensor provides a Fubini-Study metric, and its anti-symmetric sector gives a Berry curvature. Now the generalization or Quantum Modular Geometric Tensor gives a Kinematic Space and a modular Berry curvature. Here we demonstrate the emergence by focusing on a spherical entangling surface. We also use the result of the identity Virasoro block to relate the connected correlator of two Wilson lines to the two-point function of a modular Hamiltonian. This result realizes a novel holographic entanglement formula for two intervals of a general separation. This formula does not only hold for a classical gravity sector but also Quantum Gravity. The formula also provides a new Quantum Information interpretation to the connected correlators of Wilson lines as the mutual information. Our study provides an opportunity to explore Quantum Kinematic Space through Quantum Modular Geometric Tensor and hence go beyond symmetry.
arXiv comment15 pages, 1 figure
References in corpus (12)
- Towards a derivation of holographic entanglement entropy
- Quantum corrections to holographic entanglement entropy
- A Stereoscopic Look into the Bulk
- Conformal Partial Waves: Further Mathematical Results
- Entanglement, Holography and Causal Diamonds
- A universal feature of CFT Renyi entropy
- Modular Berry Connection
- A Modular Sewing Kit for Entanglement Wedges
- Quantum Correction of the Wilson Line and Entanglement Entropy in the Pure AdS Einstein Gravity Theory
- The Probe of Curvature in the Lorentzian AdS/CFT Correspondence
- Berry Curvature and Riemann Curvature in Kinematic Space with Spherical Entangling Surface
- U(1) CS Theory vs SL(2) CS Formulation: Boundary Theory and Wilson Line