Abstract
We study 2d and 3d 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 3d case there exists an integrable slicing where charge algebra takes the form of Heisenberg ⊕ \( \mathcal{A} \)3 where \( \mathcal{A} \)3 is two copies of Virasoro at Brown-Henneaux central charge for AdS3 gravity and BMS3 for the 3d flat space gravity.
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H. Adami, D. Grumiller, M.M. Sheikh-Jabbari, V. Taghiloo, H. Yavartanoo and C. Zwikel, Null boundary phase space: slicings, news & memory, JHEP 11 (2021) 155 [arXiv:2110.04218] [INSPIRE].
H. Adami, M.M. Sheikh-Jabbari, V. Taghiloo, H. Yavartanoo and C. Zwikel, Symmetries at null boundaries: two and three dimensional gravity cases, JHEP 10 (2020) 107 [arXiv:2007.12759] [INSPIRE].
H. Adami, M.M. Sheikh-Jabbari, V. Taghiloo, H. Yavartanoo and C. Zwikel, Chiral Massive News: Null Boundary Symmetries in Topologically Massive Gravity, JHEP 05 (2021) 261 [arXiv:2104.03992] [INSPIRE].
R. Ruzziconi and C. Zwikel, Conservation and Integrability in Lower-Dimensional Gravity, JHEP 04 (2021) 034 [arXiv:2012.03961] [INSPIRE].
M. Geiller, C. Goeller and C. Zwikel, 3d gravity in Bondi-Weyl gauge: charges, corners, and integrability, JHEP 09 (2021) 029 [arXiv:2107.01073] [INSPIRE].
G. Barnich and C. Troessaert, BMS charge algebra, JHEP 12 (2011) 105 [arXiv:1106.0213] [INSPIRE].
L. Freidel, R. Oliveri, D. Pranzetti and S. Speziale, Extended corner symmetry, charge bracket and Einstein’s equations, JHEP 09 (2021) 083 [arXiv:2104.12881] [INSPIRE].
J. Lee and R.M. Wald, Local symmetries and constraints, J. Math. Phys. 31 (1990) 725 [INSPIRE].
V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
R.M. Wald and A. Zoupas, A general definition of ‘conserved quantities’ in general relativity and other theories of gravity, Phys. Rev. D 61 (2000) 084027 [gr-qc/9911095] [INSPIRE].
H. Adami, D. Grumiller, S. Sadeghian, M.M. Sheikh-Jabbari and C. Zwikel, T-Witts from the horizon, JHEP 04 (2020) 128 [arXiv:2002.08346] [INSPIRE].
G. Compère, P. Mao, A. Seraj and M.M. Sheikh-Jabbari, Symplectic and Killing symmetries of AdS3 gravity: holographic vs boundary gravitons, JHEP 01 (2016) 080 [arXiv:1511.06079] [INSPIRE].
D. Grumiller, A. Pérez, M.M. Sheikh-Jabbari, R. Troncoso and C. Zwikel, Spacetime structure near generic horizons and soft hair, Phys. Rev. Lett. 124 (2020) 041601 [arXiv:1908.09833] [INSPIRE].
H. Adami, M.M. Sheikh-Jabbari, V. Taghiloo and H. Yavartanoo, Null surface thermodynamics, Phys. Rev. D 105 (2022) 066004 [arXiv:2110.04224] [INSPIRE].
G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, JHEP 05 (2010) 062 [arXiv:1001.1541] [INSPIRE].
A. Farahmand Parsa, H.R. Safari and M.M. Sheikh-Jabbari, On Rigidity of 3d Asymptotic Symmetry Algebras, JHEP 03 (2019) 143 [arXiv:1809.08209] [INSPIRE].
H.R. Safari and M.M. Sheikh-Jabbari, BMS4 algebra, its stability and deformations, JHEP 04 (2019) 068 [arXiv:1902.03260] [INSPIRE].
H.R. Safari, Deformation of Asymptotic Symmetry Algebras and Their Physical Realizations, Ph.D. thesis, IPM, Tehran, (2020). arXiv:2011.02318 [INSPIRE].
M. Enriquez-Rojo and H.R. Safari, Boundary Heisenberg algebras and their deformations, JHEP 03 (2022) 089 [arXiv:2111.13225] [INSPIRE].
D. Grumiller, M.M. Sheikh-Jabbari and C. Zwikel, Horizons 2020, Int. J. Mod. Phys. D 29 (2020) 2043006 [arXiv:2005.06936] [INSPIRE].
D. Grumiller, R. Ruzziconi and C. Zwikel, Generalized dilaton gravity in 2d, SciPost Phys. 12 (2022) 032 [arXiv:2109.03266] [INSPIRE].
D. Grumiller, R. McNees, J. Salzer, C. Valcárcel and D. Vassilevich, Menagerie of AdS2 boundary conditions, JHEP 10 (2017) 203 [arXiv:1708.08471] [INSPIRE].
L. Freidel, R. Oliveri, D. Pranzetti and S. Speziale, The Weyl BMS group and Einstein’s equations, JHEP 07 (2021) 170 [arXiv:2104.05793] [INSPIRE].
L. Ciambelli and R.G. Leigh, Isolated surfaces and symmetries of gravity, Phys. Rev. D 104 (2021) 046005 [arXiv:2104.07643] [INSPIRE].
L. Ciambelli, R.G. Leigh and P.-C. Pai, Embeddings and Integrable Charges for Extended Corner Symmetry, arXiv:2111.13181 [INSPIRE].
L. Freidel, A canonical bracket for open gravitational system, arXiv:2111.14747 [INSPIRE].
A.J. Speranza, Ambiguity resolution for integrable gravitational charges, arXiv:2202.00133 [INSPIRE].
K. Hajian and M.M. Sheikh-Jabbari, Solution Phase Space and Conserved Charges: A General Formulation for Charges Associated with Exact Symmetries, Phys. Rev. D 93 (2016) 044074 [arXiv:1512.05584] [INSPIRE].
H. Bondi, M.G.J. van der Burg and A.W.K. Metzner, Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems, Proc. Roy. Soc. Lond. A 269 (1962) 21 [INSPIRE].
R.K. Sachs, Gravitational waves in general relativity. 8. Waves in asymptotically flat space-times, Proc. Roy. Soc. Lond. A 270 (1962) 103 [INSPIRE].
R. Sachs, Asymptotic symmetries in gravitational theory, Phys. Rev. 128 (1962) 2851 [INSPIRE].
M. Campiglia and J. Peraza, Generalized BMS charge algebra, Phys. Rev. D 101 (2020) 104039 [arXiv:2002.06691] [INSPIRE].
G. Compère, A. Fiorucci and R. Ruzziconi, The Λ-BMS4 charge algebra, JHEP 10 (2020) 205 [arXiv:2004.10769] [INSPIRE].
F. Alessio, G. Barnich, L. Ciambelli, P. Mao and R. Ruzziconi, Weyl charges in asymptotically locally AdS3 spacetimes, Phys. Rev. D 103 (2021) 046003 [arXiv:2010.15452] [INSPIRE].
C. Krishnan, A. Raju and S. Roy, A Grassmann path from AdS3 to flat space, JHEP 03 (2014) 036 [arXiv:1312.2941] [INSPIRE].
G. Barnich and G. Compere, Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions, Class. Quant. Grav. 24 (2007) F15 [gr-qc/0610130] [INSPIRE].
G. Barnich, A. Gomberoff and H.A. Gonzalez, The flat limit of three dimensional asymptotically anti-de Sitter spacetimes, Phys. Rev. D 86 (2012) 024020 [arXiv:1204.3288] [INSPIRE].
G. Compère, L. Donnay, P.-H. Lambert and W. Schulgin, Liouville theory beyond the cosmological horizon, JHEP 03 (2015) 158 [arXiv:1411.7873] [INSPIRE].
J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys. 104 (1986) 207 [INSPIRE].
I. Papadimitriou and K. Skenderis, Thermodynamics of asymptotically locally AdS spacetimes, JHEP 08 (2005) 004 [hep-th/0505190] [INSPIRE].
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Adami, H., Mao, P., Sheikh-Jabbari, M.M. et al. Symmetries at causal boundaries in 2D and 3D gravity. J. High Energ. Phys. 2022, 189 (2022). https://doi.org/10.1007/JHEP05(2022)189
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DOI: https://doi.org/10.1007/JHEP05(2022)189