Non-relativistic strings and branes as non-linear realizations of Galilei groups

TL;DR

This work formulates non-relativistic strings and d-branes as Wess-Zumino terms associated with the Galilei group, using nonlinear realizations and Maurer-Cartan forms. By performing an Inönü–Wigner contraction of the Poincaré group, the authors derive a Galilei-like algebra and construct invariant forms, notably a nontrivial $\Omega_3$ whose potential $\Phi_2$ yields the NR string action. The NR string action emerges from a nontrivial third cohomology class, and its gauge-fixed form describes free transverse excitations; the approach generalizes to NR d-branes with a higher-form invariant, yielding a world-volume theory that reduces to a free field in a convenient gauge but accommodates central/topological charges. The results provide a symmetry-based foundation for NR extended objects and open directions for quantization and connections to alternative formulations such as Nambu mechanics.

Abstract

We construct actions for non-relativistic strings and membranes purely as Wess-Zumino terms of the underlying Galilei groups.