On the master space for brane brick models

• Published in: The journal of high energy physics Vol. 2023; no. 9; pp. 150 - 42
• Main Authors: Kho, Minsung, Seong, Rak-Kyeong
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 22.09.2023; Springer Nature B.V; SpringerOpen
• Subjects: Algorithms; Branes; Bricks; Classical and Quantum Gravitation; D-Branes; Differential and Algebraic Geometry; Elementary Particles; Gauge theory; High energy physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Supersymmetric Gauge Theory; Symmetry; D-Branes; Differential and Algebraic Geometry; Supersymmetric Gauge Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP09(2023)150

A bstract We systematically study the master space of brane brick models that represent a large class of 2 d (0, 2) quiver gauge theories. These 2 d (0, 2) theories are worldvolume theories of D1-branes that probe singular toric Calabi-Yau 4-folds. The master space is the freely generated space of chiral fields subject to the J - and E -terms and the non-abelian part of the gauge symmetry. We investigate several properties of the master space for abelian brane brick models with U(1) gauge groups. For example, we calculate the Hilbert series, which allows us by using the plethystic programme to identify the generators and defining relations of the master space. By studying several explicit examples, we also show that the Hilbert series of the master space can be expressed in terms of characters of irreducible representations of the full global symmetry of the master space.