Sigma Models and Phase Transitions for Complete Intersections. (4th March 2017)

• Record Type: Journal Article
• Authors: Clader, Emily; Ross, Dustin
• Is Part Of: International mathematics research notices. Volume 2018:Number 15(2018)
• Page Start: 4799
• Page End: 4851
• Publication Date: 2017-03-04
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnx029
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: 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.