Four-dimensional spectrum generating algebra for the superstring

We derive the spectrum generating algebra for the hybrid string with manifest N=1 super Poincaré symmetry in R3,1⁶. Our DDF operators establish a one-to-one correspondence with the conventional superstring spectrum, while making its four-dimensional structure manifest. We also discuss part of the antifield spectrum, and introduce a simple realization of the supersymmetry charges involving the R⁶ directions. As an application, we algebraically compute the helicity partition function. These results provide new tools for analyzing four-dimensional on-shell superspaces and may extend naturally to phenomenologically relevant compactifications.