Rak-Kyeong Seong

Abstract Reflexive polygons have attracted great interest both in mathematics and in physics. This paper discusses a new aspect of the existing study in the context of quiver gauge theories. These theories are 4d supersymmetric worldvolume theories of D3 branes with toric Calabi‐Yau moduli spaces that are conveniently described with brane tilings. We find all 30 theories corresponding to the 16 reflexive polygons, some of the theories being toric (Seiberg) dual to each other. The mesonic generat

We initiate a systematic study of 2d (0, 2) quiver gauge theories on the world-volume of D1-branes probing singular toric Calabi-Yau 4-folds. We present an algorithm for efficiently calculating the classical mesonic moduli spaces of these theories, which correspond to the probed geometries. We also introduce a systematic procedure for constructing the gauge theories for arbitrary toric singularities by means of partial resolution, which translates to higgsing in the field theory. Finally, we int

Brane brick models are Type IIA brane configurations that encode the 2d $$ \mathcal{N}=\left(0,2\right) $$ gauge theories on the worldvolume of D1-branes probing toric Calabi-Yau 4-folds. We use mirror symmetry to improve our understanding of this correspondence and to provide a systematic approach for constructing brane brick models starting from geometry. The mirror configuration consists of D5-branes wrapping 4-spheres and the gauge theory is determined by how they intersect. We also explain

We provide a brane realization of 2d (0, 2) Gadde-Gukov-Putrov triality in terms of brane brick models. These are Type IIA brane configurations that are T-dual to D1-branes over singular toric Calabi-Yau 4-folds. Triality translates into a local transformation of brane brick models, whose simplest representative is a cube move. We present explicit examples and construct their triality networks. We also argue that the classical mesonic moduli space of brane brick model theories, which corresponds

We introduce brane brick models, a novel type of Type IIA brane congurations consisting of D4-branes ending on an NS5-brane. Brane brick models are T-dual to D1-branes over singular toric Calabi-Yau 4-folds. They fully encode the innite class of 2d (generically) N = (0; 2) gauge theories on the worldvolume of the D1-branes and streamline their connection to the probed geometries. For this purpose, we also introduce new combinatorial procedures for deriving the Calabi-Yau associated to a given ga

We introduce Orbifold Reduction, a new method for generating 2d (0; 2) gauge theories associated to D1-branes probing singular toric Calabi-Yau 4-folds starting from 4d N = 1 gauge theories on D3-branes probing toric Calabi-Yau 3-folds. The new procedure generalizes dimensional reduction and orbifolding. In terms of T-dual configurations, it generates brane brick models starting from brane tilings. Orbifold reduction provides an agile approach for generating 2d (0; 2) theories with a brane reali

We introduce a new duality for $$ \mathcal{N} $$ = 1 supersymmetric gauged matrix models. This 0d duality is an order 4 symmetry, namely an equivalence between four different theories, hence we call it Quadrality. Our proposal is motivated by mirror symmetry, but is not restricted to theories with a D-brane realization and holds for general $$ \mathcal{N} $$ = 1 matrix models. We present various checks of the proposal, including the matching of: global symmetries, anomalies, deformations and the

A bstract Reflexive polytopes in n dimensions have attracted much attention both in mathematics and theoretical physics due to their connection to Fano n -folds and mirror symmetry. This work focuses on the 18 regular reflexive polytopes corresponding to smooth Fano 3-folds. For the first time, we show that all 18 regular reflexive polytopes have corresponding 2 d (0 , 2) gauge theories realized by brane brick models. These 2 d gauge theories can be considered as the worldvolume theories of D1-b

We introduce unsupervised machine learning techniques in order to identify toric phases of $4d$ $\mathcal{N}=1$ supersymmetric gauge theories corresponding to the same toric Calabi-Yau 3-fold. These $4d$ $\mathcal{N}=1$ supersymmetric gauge theories are world volume theories of a D3-brane probing a toric Calabi-Yau 3-fold and are realized in terms of a type IIB brane configuration known as a brane tiling. It corresponds to the skeleton graph of the coamoeba projection of the mirror curve associa

We study the moduli spaces of k U(N ) vortices which are realized by the Higgs branch of a U(k) supersymmetric gauge theory. The theory has 4 supercharges and lives on k D1-branes in a N D3- and NS5-brane background. We realize the vortex moduli space as a $$ {\mathbb{C}}^{*} $$ projection of the vortex master space. The Hilbert series is calculated in order to characterize the algebraic structure of the vortex master space and to identify the precise $$ {\mathbb{C}}^{*} $$ projection. As a resu