More on stubs in open string field theory

TL;DR

This paper explores modifications of open string field theory with stubs, analyzing classical solutions, gauge relations, and extending to non-BPZ even stubs, including explicit calculations for the tachyon vacuum.

Contribution

It introduces a generalized construction of A-infinity-algebras with stubs, relating different cohomomorphisms, and computes solutions for the tachyon vacuum in new settings.

Findings

Two cohomomorphisms are related by a gauge transformation and on-shell vanishing term.

The construction is extended to non-BPZ even stubs, including sliver frame stubs.

Explicit first-order solutions for the tachyon vacuum are obtained.

Abstract

We continue our analysis of open string field theory based on A-infinity-algebras obtained from Witten's theory by attaching stubs to the elementary vertex. Classical solutions of the new theory can be obtained from known analytic solutions in Witten's theory by applying a cohomomorphism. In a previous work, two such cohomomorphisms were found, one non-cyclic, obtained from the homological perturbation lemma and another cyclic one by geometric methods. Here we show that the two resulting maps are related by a combination of a gauge transformation and a term vanishing on-shell. In the second part of the paper we generalize the whole construction to non-BPZ even stubs, in particular sliver frame stubs. We discuss algebraic and geometric aspects and analyze the resulting conditions on the homotopy operator. Moreover, we explicitly calculate the first few orders of the new A-infinity-algebra solution for the tachyon vacuum in the sliver frame.