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Journal of High Energy Physics

, 2017:106 | Cite as

Brane brick models in the mirror

  • Sebastián Franco
  • Sangmin Lee
  • Rak-Kyeong Seong
  • Cumrun Vafa
Open Access
Regular Article - Theoretical Physics

Abstract

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 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 dimensions, where the order of duality is n − 1 for a Calabi-Yau n-fold. This makes us conjecture the existence of a quadrality symmetry in 0d. Finally, we comment on how the M-theory lift of brane brick models connects to the classification of 2d (0, 2) theories in terms of 4-manifolds.

Keywords

Brane Dynamics in Gauge Theories D-branes Supersymmetric gauge theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Sebastián Franco
    • 1
    • 2
  • Sangmin Lee
    • 3
    • 4
    • 5
  • Rak-Kyeong Seong
    • 6
  • Cumrun Vafa
    • 7
  1. 1.Physics DepartmentThe City College of the CUNYNew YorkU.S.A.
  2. 2.The Graduate School and University CenterThe City University of New YorkNew YorkU.S.A.
  3. 3.Center for Theoretical PhysicsSeoul National UniversitySeoulKorea
  4. 4.Department of Physics and AstronomySeoul National UniversitySeoulKorea
  5. 5.College of Liberal StudiesSeoul National UniversitySeoulKorea
  6. 6.School of PhysicsKorea Institute for Advanced StudySeoulKorea
  7. 7.Jefferson Physical LaboratoryHarvard UniversityCambridgeU.S.A.

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