Description
Abstract: Wordlvolume gauge theories arising on D-(5-2m) branes probing a toric Calabi-Yau (m+2)-fold can be uniformly encoded in objects called m-dimers. These generalize the well-known construction of 4d, N=1 theories on D-3 branes probing toric Calabi-Yau threefolds to 2d (0,2) theories on D-1 branes probing CY-4folds and 0d N=1 matrix on D-(-1) branes probing CY-5folds. The m-dimers are themselves brane configurations dual to the original setup. We explain how they simplify the passage from gauge theory to geometry and vice versa. Central to this simplification is the combinatorial description of GLSM fields parameterizing the moduli space of these gauge theories. This combinatorial description also reveals interesting relations between such theories in different dimensions, allowing us to construct some of the more complicated theories like 0d, N=1 matrix models using simpler and better understood 4d N=1 theories as the building blocks.
