Grade restriction and <i>D</i>-brane transport for a nonabelian GLSM of an elliptic curve

In this paper, we discuss a simple model for D-brane transport in nonabelian GLSMs. The model is the elliptic curve version of a nonabelian GLSM introduced by Hori and Tong and has gauge group [Formula: see text]. It has two geometric phases, both of which describe the same elliptic curve, once realized as a codimension five complete intersection in [Formula: see text] and once as a determinantal variety. The determinantal phase is strongly coupled with unbroken [Formula: see text]. There are two singular points in the moduli space where the theory has a Coulomb branch. Using grade restriction rules, we show how to transport B-branes between the two phases along paths avoiding the singular points. With the help of the GLSM hemisphere partition function, we compute analytic continuation matrices and monodromy matrices, confirming results obtained by different methods.