Establish the world-sheet-parity action on physical states non-perturbatively

Establish non-perturbatively on the world-sheet how the proposed world-sheet parity transformation acts on the physical CCY, lowest Regge trajectory, and QSC state pairs, and prove the corresponding spectral relation Δ(Ω(Ψ),−q)=Δ(Ψ,q).

Background

The paper proposes that world-sheet parity maps the mixed-flux parameter q to −q and sends each physical state to a parity-related state. Candidate parity partners are constructed for the families of states studied, and string field theory calculations provide perturbative evidence for the proposed identifications.

The authors explicitly note that the proposed state mapping has not been established non-perturbatively. A proof would promote the perturbative evidence and the assumed spectral symmetry into a rigorous world-sheet statement, strengthening the mixed-flux scaling-dimension predictions.

References

In the main text, we proposed an identification of the states related by the world-sheet parity and provided evidence for it from string field theory computations. It would be interesting to establish this identification non-perturbatively on the world-sheet and prove eq:mirror-map-spectrum-symmetry for the proposed state pairs.

— Strong coupling spectrum of $\mathrm{AdS}_3\times \mathrm{S}^3$ from string field theory  (2609.19266 - Alday et al., 16 Sep 2026) in Section 1, Introduction; proposed relation in Eq. (mirror-map-spectrum-symmetry)