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Full-Text Articles in Physical Sciences and Mathematics
Orbifold Reduction And 2d (0,2) Gauge Theories, Sebastian Franco, Sangmin Lee, Rak-Kyeong Seong
Orbifold Reduction And 2d (0,2) Gauge Theories, Sebastian Franco, Sangmin Lee, Rak-Kyeong Seong
Publications and Research
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 realization. We present three practical applications of the new algorithm: the connection between 4d Seiberg duality and 2d triality, a combinatorial method for generating theories related by …
Brane Brick Models In The Mirror, Sebastian Franco, Sangmin Lee, Rak-Kyeong Seong, Cumrun Vafa
Brane Brick Models In The Mirror, Sebastian Franco, Sangmin Lee, Rak-Kyeong Seong, Cumrun Vafa
Publications and Research
Brane brick models are Type IIA brane configurations that encode the 2d N = (0; 2) 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 how 2d (0; 2) triality is realized in terms of geometric transitions in the mirror geometry. Mirror symmetry leads to a geometric unification of dualities in different …
Stratifying On-Shell Cluster Varieties: The Geometry Of Non-Planar On-Shell Diagrams, Jacob L. Bourjaily, Sebastian Franco, Danielle Galloni, Congkao Wen
Stratifying On-Shell Cluster Varieties: The Geometry Of Non-Planar On-Shell Diagrams, Jacob L. Bourjaily, Sebastian Franco, Danielle Galloni, Congkao Wen
Publications and Research
The correspondence between on-shell diagrams in maximally supersymmetric Yang-Mills theory and cluster varieties in the Grassmannian remains largely unexplored beyond the planar limit. In this article, we describe a systematic program to survey such `on-shell varieties', and use this to provide a complete classification in the case of G(3; 6). In particular, we find exactly 24 top-dimensional varieties and 10 co-dimension one varieties in G(3; 6) | up to parity and relabeling of the external legs. We use this case to illustrate some of the novelties found for non-planar varieties relative to the case of positroids, and describe some of …
Brane Brick Models And 2d (0, 2) Triality, Sebastian Franco, Sangmin Lee, Rak-Kyeong Seong
Brane Brick Models And 2d (0, 2) Triality, Sebastian Franco, Sangmin Lee, Rak-Kyeong Seong
Publications and Research
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 to the probed Calabi-Yau 4-fold, is invariant under triality. Finally, we discuss triality in terms of phase boundaries, which play a central role in connecting …
Brane Brick Models, Toric Calabi-Yau 4-Folds And 2d (0,2) Quivers, Sebastian Franco, Sangmin Lee, Rak-Kyeong Seong
Brane Brick Models, Toric Calabi-Yau 4-Folds And 2d (0,2) Quivers, Sebastian Franco, Sangmin Lee, Rak-Kyeong Seong
Publications and Research
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 gauge theory and vice versa.
2d (0,2) Quiver Gauge Theories And D-Branes, Sebastian Franco, Dongwook Ghim, Sangmin Lee, Rak-Kyeong Seong, Daisuke Yokoyama
2d (0,2) Quiver Gauge Theories And D-Branes, Sebastian Franco, Dongwook Ghim, Sangmin Lee, Rak-Kyeong Seong, Daisuke Yokoyama
Publications and Research
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 cor-respond 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 introduce Brane Brick Models, a novel class of brane configurations that consist of D4-branes suspended from an NS5-brane wrap-ping a holomorphic surface, tessellating a 3-torus. Brane Brick Models are …