Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 5 of 5
Full-Text Articles in Physics
Graded Quivers, Generalized Dimer Models And Toric Geometry, Sebastián Franco, Azeem Hasan
Graded Quivers, Generalized Dimer Models And Toric Geometry, Sebastián Franco, Azeem Hasan
Publications and Research
The open string sector of the topological B-model on CY (m+2)-folds is described by m-graded quivers with superpotentials. This correspondence extends to general m the well known connection between CY (m+2)-folds and gauge theories on the world-volume of D(5-2m)-branes for m = 0, ..., 3. We introduce m-dimers, which fully encode the m-graded quivers and their superpotentials, in the case in which the CY (m+2)-folds are toric. Generalizing the well known m = 1,2 cases, m-dimers significantly simplify the connection between geometry and m-graded quivers. A key …
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 …
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.