Newton-Cartan D0 branes from D1 branes and integrability

Abstract We explore analytic integrability criteria for D1 branes probing 4D relativistic background with a null isometry direction. We use both the Kovacic’s algorithm of classical (non)integrability as well as the standard formulation of Lax connections to show the analytic integrability of the associated dynamical configuration. We further use the notion of double null reduction and obtain the world-volume action corresponding to a torsional Newton-Cartan (TNC) D0 brane probing a 3D torsional Newton-Cartan geometry. Moreover, following Kovacic’s method, we show the classical integrability of the TNC D0 brane configuration thus obtained. Finally, considering a trivial field redefinition for the D1 brane world-volume fields, we show the equivalence between two configurations in the presence of vanishing NS fluxes.