Nonrelativistic closed string theory

We construct a Galilean invariant nongravitational closed string theory who se excitations satisfy a nonrelativistic dispersion relation. This theory c an be obtained by taking a consistent low energy limit of any of the conven tional string theories, including the heterotic string. We give a finite fi rst order worldsheet Hamiltonian for this theory and show that this string theory has a sensible perturbative expansion, interesting high energy behav ior of scattering amplitudes and a Hagedorn transition of the thermal ensem ble. The strong coupling duals of the Galilean superstring theories are con sidered and are shown to be described by an eleven-dimensional Galilean inv ariant theory of light membrane fluctuations. A new class of Galilean invar iant nongravitational theories of light-brane excitations are obtained. We exhibit dual formulations of the strong coupling limits of these Galilean i nvariant theories and show that they exhibit many of the conventional duali ties of M theory in a nonrelativistic setting. (C) 2001 American Institute of Physics.