 Neveu–Schwarz fermionic oscillator

Antiperiodic worldsheet Majorana fermions give transverse modes $b_r^I$, $r\in \mathbb{Z}+\frac{1}{2}$, with $\{b_r^I,b_s^J\}={\delta }^{IJ}{\delta }_{r+s,0}$. Positive modes annihilate the oscillator vacuum; negative modes are fermionic creation operators.