AdS₃ Einstein gravity and boundary description: pedagogical review

Journal Article · 04 January 2024 · Classical and Quantum Gravity

DOI: https://doi.org/10.1088/1361-6382/ad17f0 · OSTI ID:2338094

Ma, Chen-Te  ^[1]

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1. Iowa State Univ., Ames, IA (United States); Pohang Univ. of Science and Technology (POSTECH) (Korea, Republic of); South China Normal University (SCNU), Guangzhou (China); University of Cape Town, Rondebosch (South Africa); Iowa State U

We review the various aspects of the 3D Einstein gravity theory with a negative cosmological constant and its boundary description. We also explore its connections to conformal field theories (CFTs), modular symmetry, and holography. It is worth noting that this particular theory is topological in nature, which means that all the physical degrees of freedom are located on the boundary. Additionally, we can derive the boundary description on a torus, which takes the form of a 2D Schwarzian theory. This observation suggests that the relevant degrees of freedom for the theory can be described using this 2D theory. Because of the renormalizability of the 3D gravity theory, one can probe the quantum regime. This suggests that it is possible to investigate quantum phenomena. Unlike the conventional CFTs, when considering the AdS₃ background, the boundary theory loses modular symmetry. This represents a departure from the usual behavior of CFT and is quite intriguing. The Weyl transformation induces anomaly in CFTs, and we indicate that applying this transformation to the 2D Schwarzian theory leads to similar results. Summing over all geometries with the asymptotic AdS₃ boundary condition is equivalent to summing over a modular group. The partition function is one-loop exact and therefore an analytical expression from the summation. This theory holds potential applications in Quantum Information and is a recurring theme in the study of holography, where gravitational theories are connected with CFTs.

• Research Organization: Iowa State Univ., Ames, IA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Nuclear Physics (NP)
• Grant/Contract Number: SC0021892
• OSTI ID: 2338094
• Journal Information: Classical and Quantum Gravity, Journal Name: Classical and Quantum Gravity Journal Issue: 2 Vol. 41; ISSN 0264-9381
• Publisher: IOP PublishingCopyright Statement
• Country of Publication: United States
• Language: English