Super-Poincare Invariant Superstring Field Theory

Using the topological techniques developed in an earlier paper with Vafa, a field theory action is constructed for any open string with critical N=2 worldsheet superconformal invariance. Instead of the Chern-Simons-like action found by Witten, this action resembles that of a Wess-Zumino-Witten model. For the N=2 string which describes (2,2) self-dual Yang-Mills, the string field generalizes the scalar field of Yang. As was shown in recent papers, an N=2 string can also be used to describe the Green-Schwarz superstring in a Calabi-Yau background. In this case, one needs three types of string fields which generalize the real superfield of the super-Yang-Mills prepotential, and the chiral and anti-chiral superfields of the Calabi-Yau scalar multiplet. The resulting field theory action for the open superstring in a Calabi-Yau background has the advantages over the standard RNS action that it is manifestly SO(3,1) super-Poincar\'e invariant and does not require contact terms to remove tree-level divergences.