Extension to General Background Deformations

Determine whether the representation-theoretic construction for open strings in a constant magnetic field can be extended to more general background deformations, including simultaneous changes of the space-time metric and the antisymmetric tensor background, so as to test how the vacuum normalization and open-string coupling combine to reconstruct the corresponding disk normalization.

Background

The paper demonstrates that, for a constant magnetic field, background-independent open-string canonical variables acquire background dependence through their mode representations. Although the associated Fock representations are unitarily inequivalent, the Bogoliubov transformation between them determines the relative vacuum normalization, which reproduces the boundary g-function and the Dirac–Born–Infeld factor.

The authors identify extension beyond constant magnetic-field deformations as an immediate unresolved direction. In particular, incorporating changes in the space-time metric together with the antisymmetric tensor background would test whether the same representation-based mechanism captures the combined effects on vacuum normalization, open-string coupling, and disk normalization.