Notes on the Wess-Zumino-Witten-like structure: L\u221e triplet and NS-NS superstring field theory

Abstract

In the NS-NS sector of superstring field theory, there potentially exist three nilpotent generators of gauge transformations and two constraint equations: it makes the gauge algebra of type II theory somewhat complicated. In this paper, we show that every NS-NS actions have their WZW-like forms, and that a triplet of mutually commutative L∞ products completely determines the gauge structure of NS-NS superstring field theory via its WZW-like structure. We give detailed analysis about it and present its characteristic properties by focusing on two NS-NS actions proposed by [1] and [2].