Topic: Birational Transformations, mass deformations and brane brick models
Speaker: Dr. Dongwook Ghim
Coordinates: PCFT C1124, 16:00, Thursday, September 11
Abstract: In this talk, we explore the interplay between birational transformations and mass deformations of (1+1)d gauge theories through their string-theoretic realization, called brane brick models. The latter is Type IIA brane configuration which describes the worldvolume theories of probe D1-branes at the toric Calabi-Yau 4-folds. We begin by reviewing how brane brick models combinatorially encode the geometric data of toric Calabi-Yau 4-folds and translate it into the physical elements of (1+1)d (0,2) supersymmetric gauge theories. We then introduce birational transformations, a new mathematical notion that transforms one Calabi-Yau geometry into another, and discuss its physics interpretation in terms of brane brick models — as mass deformations in the corresponding gauge theories. In particular, we show that the mesonic moduli spaces of brane brick models related by such mass deformations have the same number of algebraic generators and share the same Hilbert series under a specific refinement by R-symmetry, though their mesonic global symmetries may differ. Extending this perspective, we examine a broader class of birational transformations that categorize toric Calabi-Yau 4-folds and their associated gauge theories into non-trivial equivalence classes. This framework suggests a potential `Minimal Model Program' for quiver gauge theories arising from toric Calabi-Yau geometries.