Derive weighted forgetful-map identities directly from BF or BRST symmetry

Derive the global forgetful-map and pushforward identities governing the string and dilaton relations directly from BF gauge symmetry or BRST Ward identities, including the boundary and collision contributions in weighted compactifications.

Background

The paper identifies the source-free BF defect with a smooth moving marked point and uses known ordinary or weighted forgetful-map identities to reproduce the string and dilaton equations. The local BF construction supplies the operators and their normalizations, but it does not independently derive the global pushforward formulas or the contributions from weighted collision strata. Establishing such a derivation would connect the global intersection-theoretic identities more directly to BF or BRST symmetry.

References

This gives a BF interpretation of the corresponding insertions and their sewing, but not an independent derivation of the global forgetful-map and pushforward identities from local BF gauge symmetry. Deriving these identities directly from BF or BRST Ward identities remains open, as does the extension of the weighted calculation and its possible Virasoro structure to higher genus.

— Conical Defects in JT Gravity from BF Theory: Quantization, Fusion, and Weighted Moduli Spaces  (2609.03347 - Gu, 3 Sep 2026) in Section 1, Introduction, final overview paragraph before the paper organization