Open superstring field theory based on the supermoduli space

Abstract

We present a new approach to formulating open superstring field theory based on the covering of the supermoduli space of super-Riemann surfaces and explicitly construct a gauge-invariant action in the Neveu-Schwarz sector up to quartic interactions. The cubic interaction takes a form of an integral over an odd modulus of disks with three punctures and the associated ghost is inserted. The quartic interaction takes a form of an integral over one even modulus and two odd moduli, and it can be interpreted as the integral over the region of the supermoduli space of disks with four punctures which is not covered by Feynman diagrams with two cubic vertices and one propagator. As our approach is based on the covering of the supermoduli space, the resulting theory naturally realizes an $A_{\infty }$ structure, and the two-string product and the three-string product used in defining the cubic and quartic interactions are constructed to satisfy the $A_{\infty }$ relations to this order.

60 pages, 3 figures; v2: minor corrections and references added; v3: a proof that the quartic vertex is unambiguously defined for general off-shell states added in appendix A.5, version published in JHEP

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• Generalized ADHM equations from marginal deformations in open superstring field theory
• String Field Theory
• More on stubs in open string field theory
• Open superstring field theory including the Ramond sector based on the supermoduli space
• $A_{\infty }$ Action of Open $\mathcal{N}=2$ Superstring Field Theory