Intensive lectures on BH and de Sitter
Lecturer: Suvrat Raju (Prof. International Centre for Theoretical Sciences TIFR)
Date: 2023 August 31 (Thur) (1) AM 10:00-12:00 (2) PM 4:00- 6:00
September 1 (Fri) (3) AM 10:00-12:00 (4) PM 2:00- 4:00
Place: Kenkyu Honkan 3F Seminar Room (hybrid with zoom)
Lecture (1): Holography of information
We will argue that, in a theory of quantum gravity in asymptotically flat spacetime, any operator from future null infinity can be approximated arbitrarily well by an operator near the past boundary of future null infinity. This unusual property of gravity can be derived by carefully implementing the gravitational constraints in quantum mechanics. In asymptotically anti-de Sitter space, a similar argument shows that any operator in the theory can be approximated by an operator in an infinitesimal time band on the boundary. These
arguments help to explain why gravitational theories are holographic. For simple states, this property of gravity can also be verified in perturbation theory.
1) “The Holographic Nature of Null Infinity”, arXiv:2002.02448
2) “A physical protocol for observers near the boundary to obtain bulk information in quantum gravity”, arXiv: 2008.01740
September 1 (Fri) (3) AM 10:00-12:00 (4) PM 2:00- 4:00
Place: Kenkyu Honkan 3F Seminar Room (hybrid with zoom)
Lecture (1): Holography of information
We will argue that, in a theory of quantum gravity in asymptotically flat spacetime, any operator from future null infinity can be approximated arbitrarily well by an operator near the past boundary of future null infinity. This unusual property of gravity can be derived by carefully implementing the gravitational constraints in quantum mechanics. In asymptotically anti-de Sitter space, a similar argument shows that any operator in the theory can be approximated by an operator in an infinitesimal time band on the boundary. These
arguments help to explain why gravitational theories are holographic. For simple states, this property of gravity can also be verified in perturbation theory.
1) “The Holographic Nature of Null Infinity”, arXiv:2002.02448
2) “A physical protocol for observers near the boundary to obtain bulk information in quantum gravity”, arXiv: 2008.01740
Lecture (1): Holography of information
We will argue that, in a theory of quantum gravity in asymptotically flat spacetime, any operator from future null infinity can be approximated arbitrarily well by an operator near the past boundary of future null infinity. This unusual property of gravity can be derived by carefully implementing the gravitational constraints in quantum mechanics. In asymptotically anti-de Sitter space, a similar argument shows that any operator in the theory can be approximated by an operator in an infinitesimal time band on the boundary. These
arguments help to explain why gravitational theories are holographic. For simple states, this property of gravity can also be verified in perturbation theory.
1) “The Holographic Nature of Null Infinity”, arXiv:2002.02448
2) “A physical protocol for observers near the boundary to obtain bulk information in quantum gravity”, arXiv: 2008.01740
Lecture (2): Holography of information and black holes In an ordinary quantum field theory, the “split property” implies that the state of a system can be specified independently on a bounded subregion of a Cauchy slice and its complement. The principle of holography of information implies that this property does not hold for theories of gravity. The original formulation of the information paradox explicitly assumed the split property and we follow this assumption to isolate the precise error in Hawking’s argument for information loss. A similar assumption also underpins the monogamy paradox of Mathur and AMPS. We will describe how accounting for the unusual localization of information in gravity helps to resolve these puzzles.
1) “Failure of the split property in gravity and the information
paradox”, arXiv:2110.05470
2) “Lessons from the information paradox”, arXiv:2012.05770
Lecture (3) and (4): Hilbert space and holography of information in de Sitter space We obtain all solutions of the Wheeler-DeWitt equation with positive cosmological constant for a closed universe in the large-volume limit. We define a natural norm on the solution space and thereby obtain a description of the Hilbert space of quantum gravity in an asymptotically de Sitter spacetime. This provides the finite G_N generalization of the Hilbert space constructed by Higuchi using group averaging. All the states in this Hilbert space share the symmetries
of the Euclidean vacuum. We use this property to generalize the principle of holography of information to de Sitter space: cosmological correlators (defined as appropriately gauge-fixed observables) in an arbitrary small region suffice to completely specify the state.
1) “The Hilbert space of de Sitter quantum gravity”, arXiv:2303.16315
2) “Holography of information in de Sitter space”, arXiv:2303.16316
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