Ramond sector

The Ramond sector uses periodic worldsheet Majorana fermions, giving integer oscillator labels and fermionic zero modes. The zero modes obey a Clifford algebra, so their action on the ground state generates a spacetime spinor representation rather than an ordinary scalar vacuum.

This explains how a worldsheet field with a periodic boundary condition leads to spacetime fermions in the open-string spectrum. The GSO projection selects an allowed chirality in the critical construction. A closed string has separate left-moving and right-moving choices; combining Ramond and Neveu–Schwarz sectors generates the familiar type-II field sectors. Worldsheet fermionic character and spacetime spin are distinct notions connected by the zero-mode and physical-state constraints.

A worldsheet operator that changes fermion boundary conditions to the Ramond sector and creates a target spinor state. For $D$ real matter fermions its conformal weight is $D/16$. At $D=10$, combining it with the appropriate superghost factor gives a dimension-one spacetime-supersymmetry current.

In the critical RNS string, a spacetime supersymmetry generator is $Q_A=\oint e^{-{\varphi }_{\mathrm{gh}}/2}{S}_A$. The RNS spin field has weight $5/8$ and the superghost exponential has weight $3/8$, making a weight-one current. The GSO projection ensures the locality needed to act on retained vertex operators. Its operator products generate translations and relate NS sector and R sector states.

The zero-mode anticommutator $\{d_0^I,d_0^J{\}}_{+}={\delta }^{IJ}$ becomes the Euclidean Clifford algebra after ${\gamma }^I=\sqrt{2}{d}_0^I$. It acts within the oscillator-vacuum space. Eight transverse Gamma matrices give a minimal complex representation of dimension sixteen, split into two eight-dimensional chirality sectors.

For integer transverse string modes, $N_R={\sum }_{k>0}({\alpha }_{-k}\cdot {\alpha }_k+k{d}_{-k}\cdot d_k)$ with vacuum-annihilating normal ordering. Each nonzero-mode creation operator raises the level by $k$; fermionic zero modes commute with it. The open-string mass condition is $M^2=2\pi T{N}_R$, with zero Ramond intercept.