A new action for nonrelativistic bosonic string in flat space time

A new action for nonrelativistic bosonic string in flat space time is shown to emerge from a holistic Hamiltonian analysis of the minimal action for the string. The proposed action under appropriate limits interpolates between the minimal action (Nambu Goto type) where the string metric is taken to be that induced by the embedding and the Polyakov type of action where the world sheet metric components are independent fields. The equivalence among different actions is established by a detailed study of symmetries based on constraint analysis. The interpolating action mooted here is shown to reveal the geometry of the string and may be useful in analyzing the nonrelativistic string coupled with curved background.