The Galilean Superstring

TL;DR

The paper derives a Galilean (zero-tension) superstring by taking a non-relativistic limit of the Green-Schwarz string, yielding a theory with κ-symmetry and a Wess-Zumino term that introduces a central/topological charge in the Galilean SUSY algebra. This structure enforces a unitarity bound on the total momentum, $|\mathbf{P}|^2 \le (nT)^2$, with the bound saturated by half-BPS bosonic solutions that preserve part of the supersymmetry. A Hamiltonian/phase-space analysis reveals a mixed fermionic constraint structure and a gauge-fixed, explicitly supersymmetric action in the transverse sector, providing a concrete setting to study covariant quantization-like issues in a simplified non-relativistic context. The work also extends the construction to a Galilean supermembrane in higher p-brane settings and discusses the implications for non-relativistic brane dynamics and the role of central charges in ensuring unitarity.

Abstract

The action for a Galilean superstring is found from a non-relativistic limit of the closed Green-Schwarz (GS) superstring; it has zero tension and provides an example of a massless super-Galilean system A Wess-Zumino term leads to a topological central charge in the Galilean supersymmetry algebra, such that unitarity requires a upper bound on the total momentum. This Galilean-invariant bound, which is also implied by the classical phase-space constraints, is saturated by solutions of the superstring equations of motion that half-preserve supersymmetry. We discuss briefly the extension to the Galilean supermembrane.