Landau-Ginzburg models for certain fiber products with curves

TL;DR

This paper constructs non-compact Calabi-Yau threefolds as fiber products of Riemann surfaces and noncompact threefolds within hybrid Landau-Ginzburg models, connecting physical models with complex geometric structures.

Contribution

It introduces a physical realization of specific fiber product Calabi-Yau threefolds using hybrid Landau-Ginzburg models and recent GLSM techniques, linking physics and complex geometry.

Findings

Construction of fiber product threefolds with trivial canonical bundle

Matching physical conditions with mathematical constraints

Application to twistor spaces of hyperKahler four-manifolds

Abstract

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.