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Quivers, tilings and branes

Xiao, Y. (2018). Quivers, tilings and branes. (Unpublished Doctoral thesis, City, University of London)

Abstract

In this thesis, we review the history behind brane tilings and quiver gauge theories as well as recent developments within this field. The aim of this work is to present a concise introduction towards this field as well as recent new developments on their classifications. In the chapter 3, we present a classification of brane tilings purely from a geometric point of view, i.e given a toric diagram of certain area, we find a host of quiver gauge theories that have their vacuum moduli space (VMS) given by the toric geometry.

Brane tilings are bipartite periodic graphs on a torus and they are a graphic representation of 4d N = 1 supersymmetric gauge theories originating from D3-braning probing a Calabi-Yau 3-fold singularity. The combinatoric properties of toric diagrams brane tilings/dimer models make themselves the largest and richest set of supersymmetric gauge theories know so far. However, the classification of these theories still remain on the physical side and another classification based on the toric diagram of VMS is developed in this work. In particular, we classified all toric CY 3-folds with toric diagrams up to area 8 and constructed a brane tiling for each of them. To do so, we developed implementations of dimer model techniques specifically tailored for partial resolution. We also created computational modules for a wide range of manipulations and computations involving brane tilings.

Publication Type: Thesis (Doctoral)
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Departments: Doctoral Theses
Doctoral Theses > School of Mathematics, Computer Science and Engineering Doctoral Theses
School of Mathematics, Computer Science & Engineering
School of Mathematics, Computer Science & Engineering > Mathematics
URI: https://openaccess.city.ac.uk/id/eprint/22113
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