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 ∞ 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.

Localization of effective actions in open superstring field theory

“…(2.44) 3 We are not interested in O(g 3 ) terms which, in the present setting, come exclusively from the elementary cubic vertex in (2.1) and which are not affected by integrating out the heavy fields. Moreover in the cases we analize these couplings are identically vanishing due to zero momentum.…”

On the BV formalism of open superstring field theory in the large Hilbert space

“…Several differently-looking formulations of superstring field theory are currently established; these all can be embedded into the large Hilbert space and their gauge structures are understood in a unified mannerat least, at the classical level. In this process, even for a very trivial embedding of a gaugefixable theory based on the small Hilbert space, the original gauge symmetry is enlarged as (1.1c) and the Wess-Zumino-Witten-like gauge structure arises [20,[33][34][35]. Since the gauge-fixing of WZW-like string field theory has been an unsolved problem, this result implies that a gauge-fixable theory turns into a gauge-unfixable theory after the embedding -so, the BV master action should exist even in the large Hilbert space.…”

“…The large A ∞ theory is the simplest but a nontrivial example of the WZW-like open string field theory [35]: it is completely described by a pair of mutually commutative A ∞ algebras (η ; M); alternatively, it is also described by the equivalent A ∞ pair (η − * ; Q). The large A ∞ action just equals to the WZW-like action (1.1a) based on another solution of (1.1b) given by…”

“…A procedure which does not depend on these parametrisations would be necessitated to apply the BV formalism to the general WZW-like formulation [34,35].…”

Supersymmetry in open superstring field theory

“…In the large Hilbert space formulation [1] there are ambiguities in the choice of supersymmetry transformation related to the enlarged gauge symmetry of the theory, and we postpone discussion to later work [4]. 1 Since classical open superstring field theory does not contain gravity, supersymmetry can only be described as a global symmetry.…”