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We discuss a simple model for D-brane transport in non-abelian GLSMs. Themodel is the elliptic curve version of a non-abelian GLSM introduced by Horiand Tong and has gauge group U(2). It has two geometric phases, both of whichdescribe the same elliptic curve, once realised as a codimension five completeintersection in G(2,5) and once as a determinantal variety. The determinantalphase is strongly coupled with unbroken SU(2). There are two singular points inthe moduli space where the theory has a Coulomb branch. Using grade restrictionrules, we show how to transport B-branes between the two phases along pathsavoiding the singular points. With the help of the GLSM hemisphere partitionfunction we compute analytic continuation matrices and monodromy matrices,confirming results obtained by different methods.

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