Sebastian Franco (CCNY), Graded Quivers, Generalized Dimer Models and Toric Geometry

The open string sector of the topological B-model model on CY (m+2)-folds is described by m-graded quivers with superpotentials. This connection extends to general m the celebrated correspondence between CY (m+2)-folds and quantum field theories in (6-2m) dimensions. These quivers exhibit new order-(m+1) mutations, which reproduce the recently discovered dualities of the associated quantum field theories for m≤3 and generalize them to m>3. In the first part of this talk we will discuss the general framework of graded quivers, which also involves ideas on higher Ginzburg algebras and higher cluster categories.

We will then introduce m-dimers, which fully encode the m-graded quivers and their superpotentials in the case of toric CY (m+2)-folds. Generalizing the standard m=1 case, m-dimers significantly simplify the map between geometry and m-graded quivers.