Grade restriction and D-brane transport for a non-abelian GLSM of an elliptic curve

Abstract: We discuss a simple model for D-brane transport in non-abelian GLSMs. The model is the elliptic curve version of a non-abelian GLSM introduced by Hori and Tong and has gauge group U(2). It has two geometric phases, both of which describe the same elliptic curve, once realised as a codimension five complete intersection in G(2,5) and once as a determinantal variety. The determinantal phase is strongly coupled with unbroken SU(2). 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.