Recent Developments R in the Jackiw-Teitelboim Gravity Kanato Goto RIKEN iTHEMS & Cornell University
Introduction -Toward Understanding Quantum Gravity-
Quantum mechanics × General Relativity
Quantum Mechanics Wave function, partition function…. we must sum over all possible trajectories “path-integral” General Relativity Properties of gravity are represented as spacetime Quantum mechanics geometries × General Relativity
<latexit sha1_base64="PothVjf804+grfNo9hnwiZEUiEo=">ACIXicbVDLSgMxFM34rPVdekmWAQ3lpkq2I1Q1IXuKtgHdMYhk6bT0CQzJlCGeZX3Pgrblwo0p34M6YPUFsPXDg515y7wliRpW27U9raXldW09t5Hf3Nre2S3s7TdUlEhM6jhikWwFSBFGBalrqhlpxZIgHjDSDPrXY785IFLRSDzoYUw8jkJBuxQjbS/UHFril6VOjUxYjBmyz0U5cnrkgy8pie3pmX5DCUaJC1fywv8wtFu2RPABeJMyNFMEPNL4zcToQToTGDCnVduxYeymSmJGsrybKBIj3EchaRsqECfKSycXZvDYKB3YjaQpoeFE/T2RIq7UkAemkyPdU/PeWPzPaye6W/FSKuJE4GnH3UTBnUEx3HBDpUEazY0BGFJza4Q95BEWJtQ8yYEZ/7kRdIol5yzUvn+vFi9msWRA4fgCJwAB1yAKrgFNVAHGDyBF/AG3q1n69X6sEbT1iVrNnMA/sD6+gZzEKT0</latexit> Quantum Gravity..? We must sum over all possible “geometries”..? Less clear both conceptually and practically…. Z D g µ ν e − I grav [ g µ ν ] Ψ = Current understanding: mostly at semi-classical level Semi-classical analyses around the black hole background inevitably lead to paradoxes…. Quantum mechanics Hawking’s information loss problem × General Relativity AMPS’s Firewall paradox Lack of understanding the basic mechanism of quantum gravity
String theory Miraculously enables us to compute the scattering amplitude with gravitons! Definition based on the worldsheet picture : perturbation on a fixed background geometry hard to recapture the concept of spacetime geometry from the perspective of quantum mechanics
Holographic Principle -discovery of AdS/CFT Maldacena ‘97 Quantum gravity on asymptotically AdS Conformal field theory on the infinite boundary of AdS AdS spacetime would be emergent from the quantum degrees of freedom of boundary theory (=CFT) Can describe (at least outside of) the black holes CFT obeys quantum mechanical law and unitary time evolution
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