Sigma Models and Phase Transitions for Complete Intersections
We study a one parameter family of gauged linear sigma models (GLSMs) naturally associated to a complete intersection in weighted projective space. In the positive phase of the family we recover Gromov Witten theory of the complete intersection, while in the negative phase we obtain a Landau Ginzburg type theory. Focusing on the negative phase, we develop foundational properties which allow us to state and prove a genus zero comparison theorem that generalizes the multiple log canonical correspondence and should be viewed as analogous to quantum Serre duality in the positive phase. Using this comparison result, along with the crepant transformation conjecture and quantum Serre duality, we prove a genus zero correspondence between the GLSMs which arise at the two phases, thereby generalizing the Landau Ginzburg/Calabi Yau correspondence to complete intersections.