On genus-0 invariants of Calabi-Yau hybrid models

Abstract

We compute genus zero correlators of hybrid phases of Calabi-Yau gauged linear sigma models (GLSMs), i.e. of phases that are Landau-Ginzburg orbifolds fibered over some base. These correlators are generalisations of Gromov-Witten and FJRW invariants. Using previous results on the structure of the of the sphere- and hemisphere partition functions of GLSMs when evaluated in different phases, we extract the I-function and the J-function from a GLSM calculation. The J-function is the generating function of the correlators. We use the field theoretic description of hybrid models to identify the states that are inserted in these correlators. We compute the invariants for examples of one- and two-parameter hybrid models. Our results match with results from mirror symmetry and FJRW theory.

Marginal deformations of Calabi-Yau hypersurface hybrids with (2,2) supersymmetry

“…Of course there would be non-perturbative corrections to OPE of the (a,c) operators, and it would be extremely interesting to understand these directly in terms of the hybrid theory. The results obtained recently in [23] should be of use in uncovering these quantum corrections.…”

“…The result is a non-linear sigma model with target space Y , the total space of the canonical bundle O V (K V ) → V equipped with a chiral superpotential W = ΦP , where Φ is the distinguished fiber coordinate, and P is a section of the anticanonical bundle O V (−K V ) → V chosen to be suitably generic so that X = {P = 0} ⊂ V is a smooth manifold. We can think of this theory as an example of a hybrid theory, such as those introduced in [22] and recently studied in a number of works including [23]. A generic hybrid theory is constructed as a fibration of a (2,2) Landau-Ginzburg theory over a suitable base manifold V , where the Landau-Ginzburg fields are sections of certain vector bundles over V , while the Landau-Ginzburg superpotential varies holomorphically over the base.…”