Abstract
In this paper we study a family of generalizations of the Pontryagin and Husain-Kuchǎr actions on manifolds with boundary. In some cases, they describe well- known models — either at the boundary or in the bulk — such as 3-dimensional Euclidean general relativity with a cosmological constant or the Husain-Kuchǎr model. We will use Hamiltonian methods in order to disentangle the physical and dynamical content of the systems that we discuss here. This will be done by relying on a geometric implementation of the Dirac algorithm in the presence of boundaries recently proposed by the authors.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S-S. Chern and J. Simons, Characteristic Forms and Geometric Invariants, Annals Math.99 (1974) 48.
J.F. Barbero G., General Relativity as a Theory of Two Connections, Int. J. Mod. Phys.D 3 (1994) 397.
V. Husain and K.V. Kuchar, General covariance, new variables and dynamics without dynamics, Phys. Rev.D 42 (1990) 4070 [INSPIRE].
E.W. Mielke and P. Baekler, Topological gauge model of gravity with torsion, Phys. Lett.A 156 (1991) 399 [INSPIRE].
P. Baekler, E.W. Mielke and F.W. Hehl, Dynamical symmetries in topological 3D gravity with torsion, Nuovo Cim.B 107 (1992) 91 [INSPIRE].
T. Kawai, Teleparallel theory of (2 + 1)-dimensional gravity, Phys. Rev. D 48 (1993) 5668 [INSPIRE].
M. Blagojevic and M. Vasilic, Asymptotic dynamics in 3D gravity with torsion, Phys. Rev.D 68 (2003) 124007 [gr-qc/0306070] [INSPIRE].
M. Blagojevic and M. Vasilic, Asymptotic symmetries in 3D gravity with torsion, Phys. Rev.D 67 (2003) 084032 [gr-qc/0301051] [INSPIRE].
S.L. Cacciatori, M.M. Caldarelli, A. Giacomini, D. Klemm and D.S. Mansi, Chern-Simons formulation of three-dimensional gravity with torsion and nonmetricity, J. Geom. Phys.56 (2006) 2523 [hep-th/0507200] [INSPIRE].
R. Banerjee, S. Gangopadhyay, P. Mukherjee and D. Roy, Symmetries of topological gravity with torsion in the hamiltonian and lagrangian formalisms, JHEP02 (2010) 075 [arXiv:0912.1472] [INSPIRE].
M. Blagojevic and B. Cvetkovic, Conserved charges in 3D gravity, Phys. Rev.D 81 (2010) 124024 [arXiv:1003.3782] [INSPIRE].
V. Bonzom and E.R. Livine, A Immirzi-like parameter for 3D quantum gravity, Class. Quant. Grav.25 (2008) 195024 [arXiv:0801.4241] [INSPIRE].
R. Basu and S.K. Paul, 2 + 1 Quantum Gravity with Barbero-Immirzi like parameter on Toric Spatial Foliation, Class. Quant. Grav.27 (2010) 125003 [arXiv:0909.4238] [INSPIRE].
J.F. Barbero G., B. Díaz, J. Margalef-Bentabol and E.J.S. Villaseñor, Dirac’s algorithm in the presence of boundaries: a practical guide to a geometric approach, accepted for publication in Class. Quant. Grav. [arXiv:1904.11790] [INSPIRE].
M. Gotay, J. Nester and G. Hinds, Presymplectic manifolds and the Dirac-Bergmann theory of constraints, J. Math. Phys.19 (1978) 2388.
J.F. Barbero G., J. Prieto and E.J.S. Villaseñor, Hamiltonian treatment of linear field theories in the presence of boundaries: a geometric approach, Class. Quant. Grav.31 (2014) 045021 [arXiv:1306.5854] [INSPIRE].
J. Margalef-Bentabol, Towards general relativity through parametrized theories, Ph.D. Thesis (2018) [arXiv:1807.05534] [INSPIRE].
J.F. Barbero G., Reality conditions and Ashtekar variables: A Different perspective, Phys. Rev.D 51 (1995) 5498 [gr-qc/9410013] [INSPIRE].
S. Carlip, Quantum Gravity in 2 + 1 dimensions, Cambridge University Press (2003) [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv EPrint: 1906.09820
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Barbero G., J.F., Díaz, B., Margalef-Bentabol, J. et al. Generalizations of the Pontryagin and Husain-Kuchař actions to manifolds with boundary. J. High Energ. Phys. 2019, 121 (2019). https://doi.org/10.1007/JHEP10(2019)121
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2019)121