Abstract
We introduce and initiate the study of a general class of 2d \( \mathcal{N} \) = (0, 2) quiver gauge theories, defined in terms of certain 2-dimensional CW complexes on oriented 3-manifolds. We refer to this class of theories as BFT2’s. They are natural generalizations of Brane Brick Models, which capture the gauge theories on D1-branes probing toric Calabi-Yau 4-folds. The dynamics and triality of the gauge theories translate into simple transformations of the underlying CW complexes. We introduce various combinatorial tools for analyzing these theories and investigate their connections to toric Calabi-Yau manifolds, which arise as their master and moduli spaces. Invariance of the moduli space is indeed a powerful criterion for identifying theories in the same triality class. We also investigate the reducibility of these theories.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Franco, D. Ghim, S. Lee, R.-K. Seong and D. Yokoyama, 2d (0,2) Quiver Gauge Theories and D-branes, JHEP 09 (2015) 072 [arXiv:1506.03818] [INSPIRE].
S. Franco, S. Lee and R.-K. Seong, Brane Brick Models, Toric Calabi-Yau 4-Folds and 2d (0, 2) Quivers, JHEP 02 (2016) 047 [arXiv:1510.01744] [INSPIRE].
S. Franco, S. Lee and R.-K. Seong, Brane brick models and 2d (0, 2) triality, JHEP 05 (2016) 020 [arXiv:1602.01834] [INSPIRE].
S. Franco, S. Lee, R.-K. Seong and C. Vafa, Brane Brick Models in the Mirror, JHEP 02 (2017) 106 [arXiv:1609.01723] [INSPIRE].
S. Franco, S. Lee and R.-K. Seong, Orbifold Reduction and 2d (0, 2) Gauge Theories, JHEP 03 (2017) 016 [arXiv:1609.07144] [INSPIRE].
S. Franco, D. Ghim, S. Lee and R.-K. Seong, Elliptic Genera of 2d (0,2) Gauge Theories from Brane Brick Models, JHEP 06 (2017) 068 [arXiv:1702.02948] [INSPIRE].
S. Franco and A. Hasan, 3d printing of 2d \( \mathcal{N} \) = (0, 2) gauge theories, JHEP 05 (2018) 082 [arXiv:1801.00799] [INSPIRE].
S. Franco, Bipartite Field Theories: from D-brane Probes to Scattering Amplitudes, JHEP 11 (2012) 141 [arXiv:1207.0807] [INSPIRE].
S. Franco, D. Galloni and R.-K. Seong, New Directions in Bipartite Field Theories, JHEP 06 (2013) 032 [arXiv:1211.5139] [INSPIRE].
S. Franco, Cluster Transformations from Bipartite Field Theories, Phys. Rev. D 88 (2013) 105010 [arXiv:1301.0316] [INSPIRE].
S. Franco and A. Uranga, Bipartite Field Theories from D-branes, JHEP 04 (2014) 161 [arXiv:1306.6331] [INSPIRE].
S. Franco, D. Galloni and A. Mariotti, Bipartite Field Theories, Cluster Algebras and the Grassmannian, J. Phys. A 47 (2014) 474004 [arXiv:1404.3752] [INSPIRE].
S. Franco, E. García-Valdecasas and A. M. Uranga, Bipartite field theories and D-brane instantons, JHEP 11 (2018) 098 [arXiv:1805.00011] [INSPIRE].
D. Xie and M. Yamazaki, Network and Seiberg Duality, JHEP 09 (2012) 036 [arXiv:1207.0811] [INSPIRE].
J. J. Heckman, C. Vafa, D. Xie and M. Yamazaki, String Theory Origin of Bipartite SCFTs, JHEP 05 (2013) 148 [arXiv:1211.4587] [INSPIRE].
S. Franco and A. Hasan, Graded Quivers, Generalized Dimer Models and Toric Geometry, JHEP 11 (2019) 104 [arXiv:1904.07954] [INSPIRE].
S. Franco, A. Hanany, K. D. Kennaway, D. Vegh and B. Wecht, Brane dimers and quiver gauge theories, JHEP 01 (2006) 096 [hep-th/0504110] [INSPIRE].
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
F. Benini, Y. Tachikawa and B. Wecht, Sicilian gauge theories and N = 1 dualities, JHEP 01 (2010) 088 [arXiv:0909.1327] [INSPIRE].
I. Bah, C. Beem, N. Bobev and B. Wecht, Four-Dimensional SCFTs from M5-Branes, JHEP 06 (2012) 005 [arXiv:1203.0303] [INSPIRE].
E. Witten, Phases of N = 2 theories in two-dimensions, Nucl. Phys. B 403 (1993) 159 [hep-th/9301042] [INSPIRE].
H. Garcia-Compean and A. M. Uranga, Brane box realization of chiral gauge theories in two-dimensions, Nucl. Phys. B 539 (1999) 329 [hep-th/9806177] [INSPIRE].
A. Gadde, S. Gukov and P. Putrov, (0, 2) trialities, JHEP 03 (2014) 076 [arXiv:1310.0818] [INSPIRE].
K. Costello and D. Gaiotto, Vertex Operator Algebras and 3d \( \mathcal{N} \) = 4 gauge theories, JHEP 05 (2019) 018 [arXiv:1804.06460] [INSPIRE].
A. Hanany and T. Okazaki, (0, 4) brane box models, JHEP 03 (2019) 027 [arXiv:1811.09117] [INSPIRE].
D. Gaiotto and T. Okazaki, Dualities of Corner Configurations and Supersymmetric Indices, JHEP 11 (2019) 056 [arXiv:1902.05175] [INSPIRE].
T. Okazaki, Abelian dualities of \( \mathcal{N} \) = (0, 4) boundary conditions, JHEP 08 (2019) 170 [arXiv:1905.07425] [INSPIRE].
K. Mohri, D-branes and quotient singularities of Calabi-Yau fourfolds, Nucl. Phys. B 521 (1998) 161 [hep-th/9707012] [INSPIRE].
S. Franco, D. Ghim, S. Lee, R.-K. Seong and D. Yokoyama, 2d (0, 2) quiver gauge theories and d-branes, JHEP 09 (2015) 072 [arXiv:1506.03818] [INSPIRE].
S. Franco and G. Musiker, Higher Cluster Categories and QFT Dualities, Phys. Rev. D 98 (2018) 046021 [arXiv:1711.01270] [INSPIRE].
A. Postnikov, Total positivity, Grassmannians, and networks, math/0609764 [INSPIRE].
N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, A. B. Goncharov, A. Postnikov and J. Trnka, Grassmannian Geometry of Scattering Amplitudes, Cambridge University Press, Cambridge, U.K. (2016) [DOI] [arXiv:1212.5605] [INSPIRE].
D. Forcella, A. Hanany, Y.-H. He and A. Zaffaroni, The Master Space of N = 1 Gauge Theories, JHEP 08 (2008) 012 [arXiv:0801.1585] [INSPIRE].
A. Postnikov, D. Speyer and L. Williams, Matching polytopes, toric geometry, and the totally non-negative Grassmannian, J. Algebraic Combin. 30 (2009) 173.
S. Franco, D. Galloni and A. Mariotti, The Geometry of On-Shell Diagrams, JHEP 08 (2014) 038 [arXiv:1310.3820] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2107.00667
Rights and permissions
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.
About this article
Cite this article
Franco, S., Yu, X. BFT2: a general class of 2d \( \mathcal{N} \) = (0, 2) theories, 3-manifolds and toric geometry. J. High Energ. Phys. 2022, 277 (2022). https://doi.org/10.1007/JHEP08(2022)277
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2022)277