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

Algebraic Geometry Seminar

Organizers：

Caucher Birkar，贾甲

Speaker：

Rak-Kyeong Seong (UNIST)

Time：

Fri., 15:30-16:30, Mar. 7, 2025

Venue：

B725, Shuangqing Complex Building A

Online：

Zoom Meeting ID: 262 865 5007

Passcode: YMSC

Title:

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 a Calabi-Yau algebra,the center of which corresponds to the coordinate ring of a toric variety associated with a non-compact toric Calabi-Yau 4-fold. In string theory, these quivers and relations define a 2d (0,2) supersymmetric gauge theory - a worldvolume theory of a D1-brane probing the 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.

This talk is based on: https://arxiv.org/pdf/2502.08741.