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arXiv2026

Boundary observables in string field theory

Starting from the gauge invariant action for free string field theory with boundary recently constructed in 2506.05969, we define new gauge invariant observables which are analogous to the Brown-York charges of General Relativity. Just like the Brown-York charges, our observables originate from a boundary tadpole, and are associated to isometries of the SFT gauge group around a given background. The consistency of the construction requires the equation of motion of the background to be satisfied only at the boundary and therefore these observables can also be defined for backgrounds generated by sources in the bulk. As examples of our construction in open string field theory, we compute the flux through the boundary of constant electromagnetic field-strength solutions and the charge associated to the Coulomb solution. As a further example in closed string field theory, we characterize the infinite conserved charges associated to stringy-haired black-hole solutions in two-dimensional string theory. We also construct a generalization of these boundary observables to the full interacting string field theory.

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arXiv2024

A two parameter family of lightcone-like hyperbolic string vertices

We introduce a two parameter family of string field theory vertices, which we refer to as hyperbolic Kaku vertices. It is defined in terms of hyperbolic metrics on the Riemann surface, but the geometry is allowed to depend on inputs of the states. The vertices are defined for both open and closed strings. In either case, the family contains the hyperbolic vertices. Then we show that the open string lightcone vertex is obtained as the flat limit of the hyperbolic Kaku vertices. The open string Kaku vertices, which interpolate between the Witten vertex and the open string lightcone vertex, is also obtained as a flat limit. We use the same limit on the case of closed strings to define the closed string Kaku vertices: a one parameter family of vertices that interpolates between the polyhedral vertices - which are covariant, but not cubic - and the closed string lightcone vertex - which is cubic, but not Lorentz covariant.

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