<p>In this short paper we want to generalize some recent concepts related to stubs in open string field theory. First, we modify the auxiliary field method by Erbin and Firat [Open string stub as an auxiliary string field, 2023.] to sliver frame stubs which are not even with respect to the Belavin-Polyakov-Zamolodchikov (BPZ) product. We then also show that the construction is consistent at the full quantum level without any additional assumptions. Finally, we apply the method explicitly to the tachyon vacuum and the simplest identitylike solution.</p>

Czechia

Georg Stettinger

Sliver frame stubs in open string field theory via auxiliary fields

We consider Witten’s open string field theory in the presence of a non-trivial boundary of spacetime. For the kinetic term, we derive a Gibbons-Hawking-type contribution that has to be added to the action to guarantee a well-defined variational principle. The derivation is done first in a heuristic way and then confirmed by a path integral based approach using the CFT operator formalism. In the last section we discuss the boundary contributions coming from the cubic vertex, although it is problematic to apply consistent boundary conditions on the string field due to the non-locality of the vertex.

A boundary term for open string field theory

We continue our analysis of open string field theory based on -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 one by geometric methods. Here we show that to first order in the stub length the two resulting maps are related by a combination of a gauge transformation and a term vanishing on-shell. We also extend our construction to more general gauges and explicitly calculate the first few orders of the new -algebra solutions in the sliver frame.

Martin Schnabl

More on stubs in open string field theory

There are various reasons why adding stubs to the vertices of open string field theory (OSFT) is interesting: the stubs can not only tame certain singularities and make the theory more well-behaved, but also the new theory shares a lot of similarities with closed string field theory, which helps to improve our understanding of its structure and possible solutions. In this paper we explore two natural ways of implementing stubs into the framework of OSFT, resulting in an A  ∞ -algebra giving rise to infinitely many vertices. We find two distinct consistent actions, both generated by a field redefinition, interestingly sharing the same equations of motion. In the last section we illustrate their relationship and physical meaning by applying our construction to nearly marginal solutions.

Open string field theory with stubs

In this paper we will consider the most general quadratic curvature action with infinitely many covariant derivatives of massless gravity in three spacetime dimensions. The action is parity invariant and torsion-free and contains the same off-shell degrees of freedom as the Einstein-Hilbert action in general relativity. In the ultraviolet, with an appropriate choice of the propagator given by the exponential of an entire function, the point-like curvature singularity can be smoothened to a Gaussian distribution, while in the infrared the theory reduces to general relativity. We will also show how to embed new massive gravity in ghost-free infinite derivative gravity in Minkowski background as one of the infrared limits. Finally, we will provide the tree-level unitarity conditions for infinite derivative gravity in presence of a cosmological constant in deSitter and Anti-deSitter spacetimes in three dimensions by perturbing the geometries.