Null-strings Gauged, Reloaded and Quantized, I: Canonical Quantization in the Light-Cone Gauge

We study the light-cone quantization of null-strings in $D$ dimensional flat target-space. Incorporating the essential new gauge symmetry and the associated constraint structure of the null-string, allows one to solve for one more degree of freedom (DoF) compared to the standard light-cone gauge, reducing the physical phase space to $(D-3)$ propagating DoF. Quantization is formulated directly in the Schr\"odinger representation, leading to a Hilbert space of wavefunctions on the reduced configuration space. The space of physical states is built on a reduced phase space associated with the corrected gauge structure. We discuss the ground-state wavefunction and a generic class of excited states. As a direct consequence of the overlooked Carroll-Weyl gauge symmetry of the null-strings, we find the remarkable and perhaps unexpected result that null-strings exhibit a discrete spectrum. Our analysis indicate that there is no critical dimension for null-strings, and $D$ can be arbitrary.