Symmetries at causal boundaries in 2D and 3D gravity

• Published in: The journal of high energy physics Vol. 2022; no. 5; pp. 189 - 27
• Main Authors: Adami, H., Mao, Pujian, Sheikh-Jabbari, M. M., Taghiloo, V., Yavartanoo, H.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2022; Springer Nature B.V; SpringerOpen
• Subjects: Algebra; Black Holes; Boundaries; Classical and Quantum Gravitation; Elementary Particles; Freedoms; Gauge Symmetry; Global Symmetries; Gravity; High energy physics; Mathematical analysis; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Solution space; Space-Time Symmetries; Spacetime; String Theory; Symmetry; Global Symmetries; Space-Time Symmetries; Gauge Symmetry; Black Holes
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP05(2022)189

A bstract We study 2 d and 3 d gravity theories on spacetimes with causal (timelike or null) codimension one boundaries while allowing for variations in the position of the boundary. We construct the corresponding solution phase space and specify boundary degrees freedom by analysing boundary (surface) charges labelling them. We discuss Y and W freedoms and change of slicing in the solution space. For D dimensional case we find D + 1 surface charges, which are generic functions over the causal boundary. We show that there exist solution space slicings in which the charges are integrable. For the 3 d case there exists an integrable slicing where charge algebra takes the form of Heisenberg ⊕ A 3 where A 3 is two copies of Virasoro at Brown-Henneaux central charge for AdS3 gravity and BMS 3 for the 3 d flat space gravity.