Superstring Field Theory and the Wess-Zumino-Witten Action

Abstract

We describe a notion of "higher" Wess-Zumino-Witten-like action which is natural in the context of superstring field theories formulated in the large Hilbert space. For the open string, the action is characterized by a pair of commuting cyclic $A_{\infty }$ structures together with a hierarchy of higher-form potentials analogous to the Maurer-Cartan elements which appear in the conventional Wess-Zumino-Witten action. We apply this formalism to get a better understanding of symmetries of open superstring field theory and the structure of interactions in the Ramond sector, describing an interesting connection between Ramond vertices and Feynman diagrams.

v2: 63 pages, 4 figures. Minor corrections, references added

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• Marginal Solutions for the Superstring
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• Tree-level S-matrix of superstring field theory with homotopy algebra structure
• Algebraic Structures In Closed Superstring Field Theory, Homotopy Transfer And Effective Actions
• Type II superstring field theory revisited
• A consistent light-cone-gauge superstring field theory