L_infinity extensions of Galilean, Newton-Hooke and static algebras produce infinite towers of p-form fields that couple to torsionful non-Lorentzian gravities and yield WZW terms for (p-1)-branes via doubled coordinates.
Newtonian Gravity and the Bargmann Algebra
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abstract
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.
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Discusses features of non-relativistic supersymmetric field theories from Galilean and Carrollian points of view to aid construction of electric and magnetic variants.
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$L_\infty$-algebraic extensions of non-Lorentzian kinematical Lie algebras, gravities, and brane couplings
L_infinity extensions of Galilean, Newton-Hooke and static algebras produce infinite towers of p-form fields that couple to torsionful non-Lorentzian gravities and yield WZW terms for (p-1)-branes via doubled coordinates.
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Aspects of Non-Relativistic Supersymmetric Theories
Discusses features of non-relativistic supersymmetric field theories from Galilean and Carrollian points of view to aid construction of electric and magnetic variants.