Birational Transformations, Toric Calabi-Yau 4-folds and 2d (0,2) Quiver Gauge Theories

Abstract

In this talk, I will first review a generalization of quivers and relations that define in string theory a 2d (0,2) supersymmetric gauge theory - a worldvolume theory of a D1-brane probing a toric Calabi-Yau 4-fold. I will illustrate how deformations of these relations, also known as mass deformations, can be interpreted as a family of birational transformations acting on the toric varieties associated with the Calabi-Yau 4-folds. I will show that these birational transformations, first introduced by Coates et al. for toric Fano 3-folds, can be extended to a broader class of toric varieties and their corresponding 2d (0,2) supersymmetric gauge theories. At the end of my talk, I will overview the implications of our observation for families of various supersymmetric gauge theories realized in string theory. This talk is based on: https://arxiv.org/pdf/2407.19924