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Boundary conditions for internal CFTs governing D-brane spectra in type II superstrings

Develop a systematic understanding and classification of the boundary conditions allowed by internal conformal field theories that determine D-brane charges and spectra, enabling analysis of RR gauge sectors and their Weak Gravity Conjecture implications.

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Background

The authors’ proof focuses on the electric NSNS gauge sector, where fundamental string modes carry charge. Extending the analysis to RR gauge fields in type II theories requires a systematic worldsheet understanding of D-brane boundary conditions in general internal CFTs, which they identify as an open problem and defer to future work.

References

In the type II superstring case, there are also RR gauge fields to consider, for which the charged states are D-branes. To study the D-brane spectrum systematically, we would need to systemically understand the possible boundary conditions allowed by the internal CFT. We defer further discussion of this interesting open problem to.

— Proving the Weak Gravity Conjecture in Perturbative String Theory, Part I: The Bosonic String (2401.14449 - Heidenreich et al., 25 Jan 2024) in Section 4.3 (Expanding the scope of the proof)