Singular field redefinition between Witten's string field theory and Witten's theory deformed by Ellwood invariant

TL;DR

The paper investigates a singular field redefinition between Witten's open string field theory and its deformation by the Ellwood invariant, formulated within $A_ Infinity$-coalgebra language. Through a detailed construction of a cohomomorphism $F=e^{\vb{\mu}}$ and an order-by-order solution in the open-closed coupling $h$, it shows that the two theories are not physically equivalent, as the redefinition is not well-defined in general. Nevertheless, the transfer is formal and permits mapping classical solutions, most notably the tachyon vacuum, to the deformed theory, where a homotopy operator confirms the shifted BRST cohomology vanishes. This work clarifies the limitations of equivalence between the theories while highlighting a mechanism to generate deformed-theory solutions from known Witten-theory solutions, with careful interpretation of their physical meaning.

Abstract

We construct a field redefinition between Witten's string field theory and its deformation by the Ellwood invariant. This field redefinition is singular and does not imply physical equivalence between them. However, it allows us to formally transfer classical solutions of Witten's theory to solutions of the deformed theory. Although the resulting solutions are also generically singular and require careful examination of their physical interpretation, we show that the tachyon vacuum solution can be consistently transferred from Witten's theory to the deformed theory.