Review of Open Superstring Field Theory

I review the construction of an action for open superstring field theory which does not suffer from the contact term problems of other approaches. This action resembles a Wess-Zumino-Witten action and can be constructed in a manifestly D=4 super-Poincaré covariant manner. This review is based on lectures given at the ICTP LatinAmerican String School in Mexico City and the Komaba 2000 Workshop in Tokyo. e-mail: [email protected] 1 Problems with Conventional Approach The construction of a field theory action for the superstring is an important problem since it may lead to information about non-perturbative superstring theory which is unobtainable from the on-shell perturbative S-matrix. This information might be useful for understanding the non-perturbative dualities of the superstring. Although there was much activity ten years ago concerning a field theory action for the bosonic string, there was not much progress on constructing a field theory action for the superstring. After discussing the problems with conventional approaches to superstring field theory in section 1, a Wess-Zumino-Witten-like action will be constructed for open Neveu-Schwarz string field theory in section 2. In section 3, this action will be generalized to any open string with critical N=2 superconformal invariance, and section 4 will review an open superstring field theory action with manifest four-dimensional super-Poincaré covariance which includes all sectors of the superstring. The covariant string field theory action for the bosonic string is based on a BRST operator Q and a string field V of +1 ghost-number. In Witten’s approach to open string field theory, the gauge-invariant action is [1] S = 1 λ2 Tr〈 2 V QV + 1 3 V 〉 (1) where string fields are glued together at their midpoint. In generalizing this approach to superstring field theory, the main difficulty comes from the requirement that the string field carries a definite “picture”. Recall that each physical state of the superstring is represented by an infinite number of BRST-invariant vertex operators in the covariant RNS formalism [2]. To remove this infinite degeneracy, one needs to require that the vertex operator carries a definite picture, identifying which modes of the (β, γ) ghosts annihilate the vertex operator. For open superstring fields, the most common choice is that all Neveu-Schwarz (NS) string fields carry picture −1 and all Ramond (R) string fields carry picture − 2 . Since the total picture must equal −2 for open superstrings, the obvious generalization of the action (1) is [3] S = 1 λ2 Tr〈 2 VNSQVNS + 1 2 VRQY VR + 1 3 Z V 3 NS + 1 2 VNSVRVR〉 (2)