Newtonian gravity and the Bargmann algebra

Roel Andringa (1) , Eric Bergshoeff (1) , Sudhakar Panda (2) , Mees de Roo (1)

1 Centre for Theoretical Physics
2 Harish-Chandra Research Institute

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 (on-shell) Newton-Cartan theory. We discuss a few extensions of our work that are relevant in the context of the AdS-CFT correspondence.

Mots clés: Physical Sciences

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

Roel Andringa, Eric Bergshoeff, Sudhakar Panda, Mees de Roo. Newtonian gravity and the Bargmann algebra. Classical and Quantum Gravity, 2011, 28 (10), pp.105011. ⟨10.1088/0264-9381/28/10/105011⟩. ⟨hal-00699373⟩