The Ramond Sector of Open Superstring Field Theory

Although the equations of motion for the Neveu-Schwarz (NS) and Ramond (R) sectors of open superstring field theory can be covariantly expressed in terms of one NS and one R string field, picture-changing problems prevent the construction of an action involving these two string fields. However, a consistent action can be constructed by dividing the NS and R states into three string fields which are real, chiral and antichiral. The open superstring field theory action includes a WZW-like term for the real field and holomorphic Chern-Simons-like terms for the chiral and antichiral fields. Different versions of the action can be constructed with either manifest d=8 Lorentz covariance or manifest N=1 d=4 super-Poincaré covariance. The lack of a manifestly d=10 Lorentz covariant action is related to the self-dual five-form in the Type IIB R-R sector. Open superstring field theory has recently returned to center stage due to the work of Sen and others on tachyon condensation [1]. Although the Ramond sector of open superstring field theory is not directly related to tachyon condensation, an understanding of this sector is crucial for studying other properties of the superstring action. For example, it will be argued below that certain terms involving the Ramond sector are expected to satisfy non-renormalization theorems. Although a cubic open superstring field theory action involving both the Neveu-Schwarz (NS) and Ramond (R) sectors was proposed in [2], this action (as well as all others [3] constructed using picture-changing operators) suffers from problems caused by the presence of picture-raising and picture-lowering operators. The picture-raising operator appears in the NS interaction term and leads to contact-term divergences in tree-level scattering amplitudes [4]. The picture-lowering operator appears in the R kinetic term and, as will be discussed in section 2, leads to a breakdown of gauge invariance due to its nontrivial kernel. Another problem with the picture-lowering operator is that it does not commute with the b ghost and therefore cannot appear in the closed superstring kinetic term for the R-NS, NS-R or R-R sectors. As discussed in earlier papers [5] [6], the above picture-changing problems can be avoided by working in the large RNS Hilbert space [7] which includes the ξ zero mode coming from fermionizing the (β, γ) ghosts. The NS contribution to the field theory action resembles a Wess-Zumino-Witten model where the group generator g is related to the NS string field Φ by g = e Φ and …