Well-definedness of the space of worldsheet theories underlying boundary string field theory

Ascertain the mathematical well-definedness of the ‘space of worldsheet theories’ (i.e., the space of boundary Lagrangians/operators for a fixed closed-string background) on which Witten’s boundary string field theory is formulated, by resolving issues arising from ultraviolet divergences and nonrenormalizable boundary interactions.

Background

Boundary string field theory (BSFT) is presented as a formulation of open string field theory defined on the space of worldsheet boundary theories associated with a fixed closed-string background, with an action expressed in terms of BRST data of the bulk conformal field theory.

The authors note that, despite this appealing formulation, it is presently unclear how to rigorously define the underlying infinite-dimensional space of boundary theories due to potential ultraviolet divergences and the presence of nonrenormalizable boundary interactions, raising questions about the foundational underpinnings of BSFT.

References

Unfortunately, it is not clear how well-defined this space is due to worries about UV divergences and non-renormalizable boundary interactions.

— Is string field theory background independent? (2509.21159 - Krátký et al., 25 Sep 2025) in Section 5.3, Subsection "A theory on the space of theories: Witten’s BSFT"