Abstract
We investigate a class of mass deformations that connect pairs of 2d (0, 2) gauge theories associated to different toric Calabi-Yau 4-folds. These deformations are generalizations to 2d of the well-known Klebanov-Witten deformation relating the 4d gauge theories for the ℂ2/ℤ2 × ℂ orbifold and the conifold. We investigate various aspects of these deformations, including their connection to brane brick models and the relation between the change in the geometry and the pattern of symmetry breaking triggered by the deformation. We also explore how the volume of the Sasaki-Einstein 7-manifold at the base of the Calabi-Yau 4-fold varies under deformation, which leads us to conjecture that it quantifies the number of degrees of freedom of the gauge theory and its dependence on the RG scale.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Franco et al., 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, R.-K. Seong and C. Vafa, Brane brick models in the mirror, JHEP 02 (2017) 106 [arXiv:1609.01723] [INSPIRE].
S. Franco, S. Lee, R.-K. Seong and C. Vafa, Quadrality for supersymmetric matrix models, JHEP 07 (2017) 053 [arXiv:1612.06859] [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 and A. Hasan, 3d printing of 2d N = (0, 2) gauge theories, JHEP 05 (2018) 082 [arXiv:1801.00799] [INSPIRE].
S. Franco, A. Mininno, Á.M. Uranga and X. Yu, 2d N = (0, 1) gauge theories and Spin(7) orientifolds, JHEP 03 (2022) 150 [arXiv:2110.03696] [INSPIRE].
A. Hanany and K.D. Kennaway, Dimer models and toric diagrams, hep-th/0503149 [INSPIRE].
S. Franco et al., Brane dimers and quiver gauge theories, JHEP 01 (2006) 096 [hep-th/0504110] [INSPIRE].
S. Franco and R.-K. Seong, Fano 3-folds, reflexive polytopes and brane brick models, JHEP 08 (2022) 008 [arXiv:2203.15816] [INSPIRE].
S. Franco, D. Ghim and R.-K. Seong, Brane brick models for the Sasaki-Einstein 7-manifolds Yp,k(ℂℙ1 × ℂℙ1) and Yp,k(ℂℙ2), JHEP 03 (2023) 050 [arXiv:2212.02523] [INSPIRE].
I.R. Klebanov and E. Witten, Superconformal field theory on three-branes at a Calabi-Yau singularity, Nucl. Phys. B 536 (1998) 199 [hep-th/9807080] [INSPIRE].
P. Candelas, P.S. Green and T. Hubsch, Rolling among Calabi-Yau vacua, Nucl. Phys. B 330 (1990) 49 [INSPIRE].
P. Candelas and X.C. de la Ossa, Comments on conifolds, Nucl. Phys. B 342 (1990) 246 [INSPIRE].
A. Hanany and R.-K. Seong, Brane tilings and reflexive polygons, Fortsch. Phys. 60 (2012) 695 [arXiv:1201.2614] [INSPIRE].
M. Bianchi et al., Mass-deformed brane tilings, JHEP 10 (2014) 027 [arXiv:1408.1957] [INSPIRE].
E. Witten, Phases of N = 2 theories in two-dimensions, Nucl. Phys. B 403 (1993) 159 [hep-th/9301042] [INSPIRE].
D. Martelli, J. Sparks and S.-T. Yau, The geometric dual of a-maximisation for toric Sasaki-Einstein manifolds, Commun. Math. Phys. 268 (2006) 39 [hep-th/0503183] [INSPIRE].
D. Martelli, J. Sparks and S.-T. Yau, Sasaki-Einstein manifolds and volume minimisation, Commun. Math. Phys. 280 (2008) 611 [hep-th/0603021] [INSPIRE].
Y.-H. He, R.-K. Seong and S.-T. Yau, Calabi-Yau volumes and reflexive polytopes, Commun. Math. Phys. 361 (2018) 155 [arXiv:1704.03462] [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, 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 et al., Gauge theories from toric geometry and brane tilings, JHEP 01 (2006) 128 [hep-th/0505211] [INSPIRE].
D. Forcella, A. Hanany, Y.-H. He and A. Zaffaroni, Mastering the master space, Lett. Math. Phys. 85 (2008) 163 [arXiv:0801.3477] [INSPIRE].
S. Benvenuti et al., An infinite family of superconformal quiver gauge theories with Sasaki-Einstein duals, JHEP 06 (2005) 064 [hep-th/0411264] [INSPIRE].
S. Benvenuti, B. Feng, A. Hanany and Y.-H. He, Counting BPS operators in gauge theories: quivers, syzygies and plethystics, JHEP 11 (2007) 050 [hep-th/0608050] [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].
D. Forcella, A. Hanany and A. Zaffaroni, Master space, Hilbert series and Seiberg duality, JHEP 07 (2009) 018 [arXiv:0810.4519] [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 C. Romelsberger, Counting BPS operators in the chiral ring of N = 2 supersymmetric gauge theories or N = 2 braine surgery, Adv. Theor. Math. Phys. 11 (2007) 1091 [hep-th/0611346] [INSPIRE].
B. Feng, A. Hanany and Y.-H. He, Counting gauge invariants: the plethystic program, JHEP 03 (2007) 090 [hep-th/0701063] [INSPIRE].
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
D.R. Morrison and M.R. Plesser, Nonspherical horizons. 1, Adv. Theor. Math. Phys. 3 (1999) 1 [hep-th/9810201] [INSPIRE].
B.S. Acharya, J.M. Figueroa-O’Farrill, C.M. Hull and B.J. Spence, Branes at conical singularities and holography, Adv. Theor. Math. Phys. 2 (1999) 1249 [hep-th/9808014] [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].
B. Feng, Y.-H. He and F. Lam, On correspondences between toric singularities and (p, q) webs, Nucl. Phys. B 701 (2004) 334 [hep-th/0403133] [INSPIRE].
S. Cremonesi, preliminary results presented at various seminars.
Acknowledgments
S.F. is supported by the U.S. National Science Foundation grants PHY-2112729 and DMS-1854179. D.G. is supported by the Basic Science Research Program of the National Research Foundation of Korea (NRF) under the Ministry of Education in Korea (NRF-2022R1A6A3A03068148), and by JST PRESTO Grant Number JPMJPR2117. D.G. would like to thank UNIST where this project was initiated. G.G. is supported by a Simons Foundation grant for the Initiative for the Theoretical Sciences at the CUNY Graduate Center. R.-K. S. is supported by a Basic Research Grant of the National Research Foundation of Korea (NRF-2022R1F1A1073128). He is also supported by a Start-up Research Grant for new faculty at UNIST (1.210139.01), a UNIST AI Incubator Grant (1.230038.01) and UNIST UBSI Grants (1.220123.01, 1.230065.01), as well as an Industry Research Project (2.220916.01) funded by Samsung SDS in Korea. He is also partly supported by the BK21 Program (“Next Generation Education Program for Mathematical Sciences”, 4299990414089) funded by the Ministry of Education in Korea and the National Research Foundation of Korea (NRF). S.F. and R.-K. S. are grateful to the Simons Center for Geometry and Physics for hospitality during the project.
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: 2307.03220
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., Ghim, D., Goulas, G.P. et al. Mass deformations of brane brick models. J. High Energ. Phys. 2023, 176 (2023). https://doi.org/10.1007/JHEP09(2023)176
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2023)176