Residue analysis after adding a hypermultiplet to the symplectic Grassmannian theory

Determine whether additional residue contributions arise in the Coulomb-branch contour integral after adding the extra hypermultiplet proposed to correct the anti-symmetric-tensor contribution to the Bethe Ansatz equations for the odd tangent bundle of the symplectic Grassmannian.

Background

The paper compares the semiclassical twisted F-term equations of the three-dimensional U(k)\mathrm{U}(k) GLSM for the odd tangent bundle of the symplectic Grassmannian with the Bethe Ansatz equations of an open spin chain. The anti-symmetric tensor contribution does not initially match the corresponding spin-chain factor.

The authors propose adding another hypermultiplet, whose contribution corrects this particular mismatch. However, the modified theory may introduce additional poles and residue contributions to the contour integral, and the paper does not determine whether or how those contributions affect the resulting partition function and its identification with the relevant I-function.

References

In this case, we may have additional residue contributions to the contour integral due to this hypermultiplet factor.

— Revisiting three-dimensional GLSMs and K-theoretic I-functions  (2609.31273 - Kimura et al., 25 Sep 2026) in Section 5, subsection “\(\Pi T\!\operatorname{SG}(k,2n)\)”