Landau-Ginzburg models for certain fiber products with curves

In this paper we describe a physical realization of a family of non-compact Kahler threefolds with trivial canonical bundle in hybrid Landau-Ginzburg models, motivated by some recent non-Kahler solutions of Strominger systems, and utilizing some recent ideas from GLSMs. We consider threefolds given as fiber products of compact genus g Riemann surfaces and noncompact threefolds. Each genus g Riemann surface is constructed using recent GLSM tricks, as a double cover of P^1 branched over a degree 2g + 2 locus, realized via nonperturbative effects rather than as the critical locus of a superpotential. We focus in particular on special cases corresponding to a set of Kahler twistor spaces of certain hyperKahler four-manifolds, specifically the twistor spaces of R^4, C^2/Z_k, and S^1 x R^3. We check in all cases that the condition for trivial canonical bundle arising physically matches the mathematical constraint.