Determine whether the worldsheet structures admit the deformation

Determine whether the worldsheet structures associated with Courant algebroids—particularly the AKSZ-contact sigma-model structures and the associated current algebras—deform compatibly with the normal-ordered Moyal–Weyl deformation quantisation of the underlying Poisson algebra.

Background

The paper proposes interpreting the auxiliary degree-2 coordinate as a contactification of the QP2-manifold, potentially leading through AKSZ-contact geometry to sigma-models governed by Courant–Jacobi algebroids. It also notes that current algebras associated with Courant algebroids and brane-current constructions are based on the Poisson algebra that is deformed in the paper.

Whether these worldsheet constructions inherit a compatible deformation is not resolved; the authors identify this as a concrete question for future investigation.

References

Since our deformation quantises precisely the Poisson algebra underlying both constructions, a natural question is whether these worldsheet structures deform along with it, perhaps along the lines of .

— Tensor hierarchy from deformation quantisation  (2609.10692 - Hassler et al., 9 Sep 2026) in Section 'Conclusion and outlook', subsection 'Future directions', paragraph 'Worldsheet interpretation'