Gauged Linear Sigma Model and Noncommutative Resolution for Homological Projective Duality
Time: 2021-12-06
Published By: Wenqiong Li
Speaker(s): Jirui Guo(Tsinghua University)
Time: 14:00-15:00 December 7, 2021
Venue: Room 29, Quan Zhai, BICMR
Homological projective duality (HPD) is a duality between the derived categories of two (possibly noncommutative) projective varieties. Given a projective embedding, the HPD category is defined as a subcategory of the derived category of the corresponding universal hyperplane section. The HPD pair enjoys nice properties with respect to mutually orthogonal linear sections of the ambient projective spaces. Since derived categories are realized as B-branes in two-dimensional supersymmetric field theories, it is natural to expect that HPD can also be described by such theories, in particular gauged linear sigma models (GLSMs). In this talk, I will describe how to contruct a GLSM for the universal hyperplane section such that the Higgs branch (given by a Landau-Ginzburg (LG) model) of one of its phases reproduces the homological projective dual. I will also talk about how to use this construction to translate the LG description of HPD into a geometric description in terms of the derived categories of noncommutative resolutions. The structure sheaves of these noncommutative spaces turn out to be sheaves of A-infinity algebras, whereas the B-branes correspond to sheaves of A-infinity modules.
