Anomalous gravitation and its positivity from entanglement

Abstract

We explore the emergence of gravitation from entanglement in holographic CFTs with gravitational anomalies. More specifically, the holographic correspondence between topologically massive gravity (TMG) with gravitational Chern-Simons term in the 3D bulk and its dual CFT with unbalanced left and right moving central charges on the 2D boundary, is studied from the quantum entanglement perspective. Using the first law of entanglement, we derive the holographic dictionary of the energy-momentum tensor in TMG, including the chiral case with logarithmic mode. Furthermore, we show that the linearized equation of motion of TMG can also be obtained from entanglement using the Wald-Tachikawa covariant phase space formalism. Finally, we identify a quasi-local gravitational energy in the entanglement wedge as the holographic dual of relative entropy in gravitationally anomalous CFTs. The positivity and monotonicity of relative entropy imply that such a gravitational energy should be positive definite and become larger when increasing the size of the entanglement wedge. These constraints from quantum information may be potentially used to discuss the UV inconsistent issues of TMG.

Entanglement contour and modular flow from subset entanglement entropies

“…However, the construction of the Rindler transformations will be much more complicated. The explicit bulk modular flow in this background is obtained in [18] using other tricks. Constructing modular planes directly in the entanglement wedge following the bulk and boundary modular flows seems to be tough and unwise.…”

“…Even for the case of CFT 2 in a thermal state, the construction of the Rindler transformations has not been carried out yet. Nevertheless the modular flow in this case is carried out in [18] using other tricks.…”

“…Based on this property we propose a simple prescription to generate the local modular flows from only the entanglement entropies in two-dimensional theories. Based on the Rindler method [13,14,17], the modular flows for several holographic theories were previously carried out in [14,15,18]. Our prescription can reproduce the modular flows in a much easier way without refer to the Rindler transformations.…”

Modular Hamiltonians in flat holography and (W)AdS/WCFT

“…The modular Hamiltonian has been useful in several aspects of the AdS/CFT correspondence, including the derivation of holographic entanglement entropy [3], verifying the first law and various entropy inequalities [4][5][6], deriving the gravitational equations of motion from entanglement [7][8][9][10], proving the averaged and quantum null energy conditions [11][12][13][14], and generating explicit prescriptions for bulk reconstruction [15][16][17][18][19]. Considering the significant role of the modular Hamiltonian in the AdS/CFT correspondence, we would like to extend this and related concepts to models of holography beyond AdS/CFT.…”

Complexity and emergence of warped AdS3 space-time from chiral Liouville action

“…In [80], the emergence of gravitation from entanglement in holographic CFTs which have a gravitational anomaly (with unbalanced left and right moving central charges) has been studied. The Wald-Tachikawa covariant phase space formalism has been implemented there in order to obtain the linearized equations of motion of TMG from the entanglement.…”