Relevance of U(1)_{-1/2} quantization to quantum elliptic cohomology

Determine whether U(1)_{-1/2} quantization is as relevant for quantum elliptic cohomology as it is for quantum K theory.

Background

For the projective-space computation, the deformation parameter k is set to the U(1)_{-1/2} quantization value, which produces the cleanest match between the Coulomb-branch critical locus and the proposed quantum elliptic cohomology relation. In quantum K theory, the analogous quantization has a well-understood role, but the paper leaves unresolved whether the same choice has comparable mathematical or physical significance in quantum elliptic cohomology.

References

Whether $U(1)_{-1/2}$ quantization is as relevant for quantum elliptic cohomology as it is for quantum K theory, is left for future work.

Towards quantum elliptic cohomology from GLSMs  (2609.09277 - Cao et al., 8 Sep 2026) in Section 3, Quantum elliptic cohomology