Abstract
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 Calabi-Yau 4-folds to brane brick models.
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References
F. Benini and N. Bobev, Exact two-dimensional superconformal R-symmetry and c-extremization, Phys. Rev. Lett. 110 (2013) 061601 [arXiv:1211.4030] [INSPIRE].
F. Benini and N. Bobev, Two-dimensional SCFTs from wrapped branes and c-extremization, JHEP 06 (2013) 005 [arXiv:1302.4451] [INSPIRE].
A. Gadde, S. Gukov and P. Putrov, Exact Solutions of 2d Supersymmetric Gauge Theories, arXiv:1404.5314 [INSPIRE].
A. Gadde, Holomorphy, triality and non-perturbative β-function in 2d supersymmetric QCD, arXiv:1506.07307 [INSPIRE].
D. Kutasov and J. Lin, (0,2) Dynamics From Four Dimensions, Phys. Rev. D 89 (2014) 085025 [arXiv:1310.6032] [INSPIRE].
D. Kutasov and J. Lin, (0,2) ADE Models From Four Dimensions, arXiv:1401.5558 [INSPIRE].
A. Gadde, S. Gukov and P. Putrov, Fivebranes and 4-manifolds, arXiv:1306.4320 [INSPIRE].
A. Gadde, S. Gukov and P. Putrov, (0, 2) trialities, JHEP 03 (2014) 076 [arXiv:1310.0818] [INSPIRE].
N. Seiberg, Electric-magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [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].
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].
R. Tatar, Geometric Constructions of Two Dimensional (0,2) SUSY Theories, Phys. Rev. D 92 (2015) 045006 [arXiv:1506.05372] [INSPIRE].
F. Benini, N. Bobev and P.M. Crichigno, Two-dimensional SCFTs from D3-branes, arXiv:1511.09462 [INSPIRE].
S. Schäfer-Nameki and T. Weigand, F-theory and 2d (0,2) Theories, arXiv:1601.02015 [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].
B. Feng, A. Hanany and Y.-H. He, D-brane gauge theories from toric singularities and toric duality, Nucl. Phys. B 595 (2001) 165 [hep-th/0003085] [INSPIRE].
B. Feng, A. Hanany and Y.-H. He, Phase structure of D-brane gauge theories and toric duality, JHEP 08 (2001) 040 [hep-th/0104259] [INSPIRE].
C.E. Beasley and M.R. Plesser, Toric duality is Seiberg duality, JHEP 12 (2001) 001 [hep-th/0109053] [INSPIRE].
B. Feng, A. Hanany, Y.-H. He and A.M. Uranga, Toric duality as Seiberg duality and brane diamonds, JHEP 12 (2001) 035 [hep-th/0109063] [INSPIRE].
E. Witten, Phases of N = 2 theories in two-dimensions, Nucl. Phys. B 403 (1993) 159 [hep-th/9301042] [INSPIRE].
M. Futaki and K. Ueda, Tropical coamoeba and torus-equivariant homological mirror symmetry for the projective space, [arXiv:1001.4858].
K. Mohri, D-branes and quotient singularities of Calabi-Yau fourfolds, Nucl. Phys. B 521 (1998) 161 [hep-th/9707012] [INSPIRE].
F. Benini, D.S. Park and P. Zhao, Cluster Algebras from Dualities of 2d \( \mathcal{N} = \left(2,\;2\right) \) Quiver Gauge Theories, Commun. Math. Phys. 340 (2015) 47 [arXiv:1406.2699] [INSPIRE].
B. Feng, S. Franco, A. Hanany and Y.-H. He, Symmetries of toric duality, JHEP 12 (2002) 076 [hep-th/0205144] [INSPIRE].
A. Hanany and D. Vegh, Quivers, tilings, branes and rhombi, JHEP 10 (2007) 029 [hep-th/0511063] [INSPIRE].
B. Feng, Y.-H. He, K.D. Kennaway and C. Vafa, Dimer models from mirror symmetry and quivering amoebae, Adv. Theor. Math. Phys. 12 (2008) 489 [hep-th/0511287] [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].
S. Franco, A. Hanany, D. Martelli, J. Sparks, D. Vegh and B. Wecht, Gauge theories from toric geometry and brane tilings, JHEP 01 (2006) 128 [hep-th/0505211] [INSPIRE].
A.B. Goncharov and R. Kenyon, Dimers and cluster integrable systems, arXiv:1107.5588 [INSPIRE].
S. Franco, Dimer Models, Integrable Systems and Quantum Teichmüller Space, JHEP 09 (2011) 057 [arXiv:1105.1777] [INSPIRE].
R. Eager, S. Franco and K. Schaeffer, Dimer Models and Integrable Systems, JHEP 06 (2012) 106 [arXiv:1107.1244] [INSPIRE].
M. Yamazaki, Quivers, YBE and 3-manifolds, JHEP 05 (2012) 147 [arXiv:1203.5784] [INSPIRE].
S. Franco, D. Galloni and Y.-H. He, Towards the Continuous Limit of Cluster Integrable Systems, JHEP 09 (2012) 020 [arXiv:1203.6067] [INSPIRE].
M. Yamazaki and W. Yan, Integrability from 2d \( \mathcal{N} = \left(2,2\right) \) dualities, J. Phys. A 48 (2015) 394001 [arXiv:1504.05540] [INSPIRE].
S. Franco, Y. Hatsuda and M. Mariño, Exact quantization conditions for cluster integrable systems, arXiv:1512.03061 [INSPIRE].
A.B. Zamolodchikov, Tetrahedron Equations and the Relativistic S Matrix of Straight Strings in (2+1)-dimensions, Commun. Math. Phys. 79 (1981) 489 [INSPIRE].
A. Gadde, S. Gukov and P. Putrov, Walls, Lines and Spectral Dualities in 3d Gauge Theories, JHEP 05 (2014) 047 [arXiv:1302.0015] [INSPIRE].
A. Gadde and S. Gukov, 2d Index and Surface operators, JHEP 03 (2014) 080 [arXiv:1305.0266] [INSPIRE].
F. Benini, R. Eager, K. Hori and Y. Tachikawa, Elliptic genera of two-dimensional N = 2 gauge theories with rank-one gauge groups, Lett. Math. Phys. 104 (2014) 465 [arXiv:1305.0533] [INSPIRE].
F. Benini, R. Eager, K. Hori and Y. Tachikawa, Elliptic Genera of 2d \( \mathcal{N}=2 \) Gauge Theories, Commun. Math. Phys. 333 (2015) 1241 [arXiv:1308.4896] [INSPIRE].
S.H. Katz and E. Sharpe, Notes on certain (0,2) correlation functions, Commun. Math. Phys. 262 (2006) 611 [hep-th/0406226] [INSPIRE].
R. Donagi, J. Guffin, S. Katz and E. Sharpe, A Mathematical Theory of Quantum Sheaf Cohomology, Asian J. Math. 18 (2014) 387 [arXiv:1110.3751] [INSPIRE].
R. Donagi, J. Guffin, S. Katz and E. Sharpe, Physical aspects of quantum sheaf cohomology for deformations of tangent bundles of toric varieties, Adv. Theor. Math. Phys. 17 (2013) 1255 [arXiv:1110.3752] [INSPIRE].
J. Guo, B. Jia and E. Sharpe, Chiral operators in two-dimensional (0,2) theories and a test of triality, JHEP 06 (2015) 201 [arXiv:1501.00987] [INSPIRE].
A. Adams, J. Distler and M. Ernebjerg, Topological heterotic rings, Adv. Theor. Math. Phys. 10 (2006) 657 [hep-th/0506263] [INSPIRE].
S. Franco, D. Ghim, S. Lee and R.-K. Seong, to appear.
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Franco, S., Lee, S. & Seong, RK. Brane brick models and 2d (0, 2) triality. J. High Energ. Phys. 2016, 20 (2016). https://doi.org/10.1007/JHEP05(2016)020
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DOI: https://doi.org/10.1007/JHEP05(2016)020