Twisted Virasoro constraints for flat gerbes

Prove the Virasoro constraints for Gromov–Witten theories twisted by flat -gerbes arising from gerbes with trivial band over effective orbifold curves, thereby extending the Virasoro theorem beyond the essentially trivial gerbe case.

Background

The paper proves Virasoro constraints for smooth projective effective orbifold curves, whose generic stabilizer is trivial. It then discusses extending the result to smooth proper one-dimensional Deligne–Mumford stacks with nontrivial generic stabilizer by applying gerbe decomposition.

For a general gerbe with trivial band, gerbe decomposition leads to Gromov–Witten theories twisted by flat gerbes. Establishing Virasoro constraints for these twisted theories is identified as the additional unresolved step needed to obtain the corresponding result for general gerbes.

References

For a general gerbe with trivial band, the same reduction produces Gromov--Witten theories twisted by flat *-gerbes; proving the corresponding twisted Virasoro constraints is the additional step required to extend the theorem to that case. We do not prove that twisted extension in this paper.

— Virasoro Constraints for Orbifold Curves  (2609.01300 - Hu et al., 1 Sep 2026) in Section 1, subsection “Main theorem and proof strategy,” Remark following the proof strategy