Description
Abstract: Engineering quantum field theories in String Theory in terms of branes is a powerful approach for understanding their dynamics. In the first part of my talk I will introduce Brane Brick Models, a novel class of brane configurations that streamline the connection between an infinite class of 2d quiver gauge theories and toric Calabi-Yau (CY) 4-folds. Brane Brick Models can be regarded as 3d generalizations of dimer models. I will also explain how they can be systematically constructed from the underlying CY 4-fold using mirror symmetry.
Finally, I will present a unified mathematical framework based on m-graded quivers with superpotentials that elegantly describes SUSY gauge theories in even dimension, ranging from 6d to 0d, and their dualities. These quivers enjoy new, higher order mutations, which precisely correspond to the order (m+2) dualities of the corresponding gauge theories. This construction also leads to an infinite of tower of graded quivers associated to higher dimensional CYs.
