Superstring Fermion Vertex and Gauge Symmetry in Four Dimensions

Abstract

In superstring theory, the conformal fields which correspond to the ground states in the Ramond sector are the spin fields. Our objective is to discuss the properties of these operators, and the four-dimensional nature of the fermion wavefunction which labels the states. We show how the choice of the supercurrent determines the gauge symmetry charges of these massless Ramond ground states. In sect. 2, we describe the BRST expressions of their vertex operators, including the ghost fields in bosonized form; and relate BRST invariance for states in the canonical ghost picture to the physical state gauge conditions of the old covariant formalism. In sect. 3, we compute examples of tree amplitudes. We present a non-standard choice of BRST vertex operators which allow the massless Ramond states to carry non-zero charge under a Yang-Mills gauge symmetry. The BRST invariance of these operators is shown to depend on the ability to define an appropriate supercurrent. In sect. 4, we present alternative constructions of the supercurrent which satisfy the super Virasoro world sheet symmetry with shifted central charge.