(m, n)-string and D1-brane in stringy Newton-Cartan background

This paper is devoted to the analysis of (m, n)-string in stringy Newton-Cartan background. We start with the Hamiltonian constraint for (m, n)-string in general background and perform limiting procedure on metric and NSNS and Ramond-Ramond two form background that leads to stringy Newton-Cartan gravity. We also analyze conditions that these background fields have to obey in order to define consistent world-sheet (m, n)−theory. We also discuss D1-brane with dynamical electric field in stringy Newton-Cartan gravity.