Newtonian gravity and the Bargmann algebra
By Roel Andringa, Eric Bergshoeff, Sudhakar Panda, Mees de Roo. 2010
224 citations recorded by the source corpus.
We show how the Newton–Cartan formulation of Newtonian gravity can be obtained from gauging the Bargmann algebra, i.e. the centrally extended Galilean algebra. In this gauging procedure several curvature constraints are imposed. These convert the spatial (time) translational symmetries of the algebra into spatial (time) general coordinate transformations and make the spin connection gauge fields dependent. In addition we require two independent vielbein postulates for the temporal and spatial directions. In the final step we impose an additional curvature constraint to establish the connection with the (on-shell) Newton–Cartan theory. We discuss a few extensions of our work that are relevant in the context of the AdS–CFT correspondence.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/cd5f957db2f72951eb1faa1bc1a473f4c2a38b3c
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Citations in the corpus
- Dynamics of Carroll particles (2014, unknown): “7) following the same gauging procedure that in the case of the Bargmann algebra leads to Newton–Cartan gravity [24, 25] and see how far we can get.”
- Hořava-Lifshitz gravity from dynamical Newton-Cartan geometry (2015, methodology): “In section 4, we go one step further and add the central element (N) to the Galilean algebra, and consider the gauging of the resulting Bargmann algebra (as also considered in [22] for the case with no torsion).”
- Boundary stress-energy tensor and Newton-Cartan geometry in Lifshitz holography (2013, methodology): “56) the vielbein postulates (dropping the superscript T as there is no torsion) [50]”
- Gauging the Carroll algebra and ultra-relativistic gravity (2015, methodology): “In the case of the gauging of the Bargmann algebra imposing curvature constraints (without introducing new fields) to write the Galilean boost and spatial rotation connections in terms of the vielbeins and the central charge gauge connection is only possible when there is no torsion [25].”
- Towards Classification of Fracton Phases: The Multipole Algebra (2018, methodology): “We note in passing that the generators fTi; Rij;P;P1;P2g form the Bargmann algebra [68], where the spatial translations Ti correspond to the Galilean boosts, linear shifts P1 correspond to the spatial translations, P 0 2 to the Hamiltonian, and P to the mass central charge.”
- Torsional Newton–Cartan geometry and the Schrödinger algebra (2014, methodology): “In this section we will perform the gauging of the Schrödinger algebra with dynamical exponent z = 2, along similar lines as was done for the Bargmann algebra in [47, 48].”
- ‘Stringy’ Newton–Cartan gravity (2012, methodology): “the centrally extended Galilei algebra, will only be discussed at the level of the symmetries; for full details, we refer to [5].”
- Lifshitz holography (2015, background): “This section follows in particular [134, 121]; see also [135, 136, 137, 138, 139].”