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Title:
Phases of 3d GLSMs to the Grassmannian
Speaker:
Abstract:
The ordinary 2d GLSM to the complex Grassmannian manifold Gr(N,F) is a U(N) supersymmetric gauge theory with F fundamental chiral multiplets. We will revisit the 3d N=2 supersymmetric version of this theory. The 3d U(N) theory is specified by two Chern-Simons levels (k, l). We will first discuss the vacuum structure for generic (k,l), uncovering a rich pattern of Higgs, topological and hybrid phases. We will then restrict ourselves to values of (k,l) in which only a pure Higgs phase exists, giving us the Grassmannian Gr(N,F). We will analyse the half-BPS line operators in those theories in some detail. In particular, we will construct new families of line operators that flow to Schubert classes, and we will compute their fusion ring using supersymmetric localisation. In some special case, this reproduces known (physics and maths) results for the quantum K-theory of Gr(N,F). We will also comment on a 3d analogue of the standard 2d LG/CY correspondence as we vary the FI parameter from positive to negative.
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