Abstract
We study orientifold projections of families of four-dimensional \( \mathcal{N} \) = 1 toric quiver gauge theories. We restrict to quivers that have the unusual property of being associated with multiple periodic planar diagrams which give rise, in general, to inequivalent models. A suitable orientifold projection relates a subfamily of the latter by conformal duality. That is, there exist exactly marginal deformations that connect the projected models. The deformations take the form of a sign flip in some of the superpotential interactions, similarly to the β-deformation of \( \mathcal{N} \) = 4 SYM. Our construction generalizes previous results on the orientifold projections of the PdP3b and PdP3c singularities.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
B. Kol, On conformal deformations, JHEP 09 (2002) 046 [hep-th/0205141] [INSPIRE].
S. Benvenuti and A. Hanany, Conformal manifolds for the conifold and other toric field theories, JHEP 08 (2005) 024 [hep-th/0502043] [INSPIRE].
B. Kol, On conformal deformations II, arXiv:1005.4408 [INSPIRE].
D. Green et al., Exactly marginal deformations and global symmetries, JHEP 06 (2010) 106 [arXiv:1005.3546] [INSPIRE].
S.S. Razamat and G. Zafrir, N = 1 conformal dualities, JHEP 09 (2019) 046 [arXiv:1906.05088] [INSPIRE].
G. Zafrir, An N = 1 Lagrangian for the rank 1 E6 superconformal theory, JHEP 12 (2020) 098 [arXiv:1912.09348] [INSPIRE].
G. Zafrir, An N = 1 Lagrangian for an N = 3 SCFT, JHEP 01 (2021) 062 [arXiv:2007.14955] [INSPIRE].
S.S. Razamat and G. Zafrir, N = 1 conformal duals of gauged En MN models, JHEP 06 (2020) 176 [arXiv:2003.01843] [INSPIRE].
S.S. Razamat, E. Sabag and G. Zafrir, Weakly coupled conformal manifolds in 4d, JHEP 06 (2020) 179 [arXiv:2004.07097] [INSPIRE].
I.G. Etxebarria, B. Heidenreich, M. Lotito and A.K. Sorout, Deconfining N = 2 SCFTs or the art of brane bending, JHEP 03 (2022) 140 [arXiv:2111.08022] [INSPIRE].
S.S. Razamat, E. Sabag, O. Sela and G. Zafrir, Aspects of 4d supersymmetric dynamics and geometry, arXiv:2203.06880 [INSPIRE].
A. Amariti and S. Rota, An intertwining between conformal dualities and ordinary dualities, arXiv:2211.12800 [INSPIRE].
A. Antinucci, S. Mancani and F. Riccioni, Infrared duality in unoriented pseudo del Pezzo, Phys. Lett. B 811 (2020) 135902 [arXiv:2007.14749] [INSPIRE].
A. Antinucci, M. Bianchi, S. Mancani and F. Riccioni, Suspended fixed points, Nucl. Phys. B 976 (2022) 115695 [arXiv:2105.06195] [INSPIRE].
A. Amariti, M. Fazzi, S. Rota and A. Segati, Conformal S-dualities from O-planes, JHEP 01 (2022) 116 [arXiv:2108.05397] [INSPIRE].
A. Amariti et al., N = 1 conformal dualities from unoriented chiral quivers, JHEP 09 (2022) 235 [arXiv:2207.10100] [INSPIRE].
S. Franco et al., Dimers and orientifolds, JHEP 09 (2007) 075 [arXiv:0707.0298] [INSPIRE].
M. Bianchi et al., Mass-deformed brane tilings, JHEP 10 (2014) 027 [arXiv:1408.1957] [INSPIRE].
M. Bianchi, D. Bufalini, S. Mancani and F. Riccioni, Mass deformations of unoriented quiver theories, JHEP 07 (2020) 015 [arXiv:2003.09620] [INSPIRE].
R.G. Leigh and M.J. Strassler, Exactly marginal operators and duality in four-dimensional N = 1 supersymmetric gauge theory, Nucl. Phys. B 447 (1995) 95 [hep-th/9503121] [INSPIRE].
E. Barnes, K.A. Intriligator, B. Wecht and J. Wright, Evidence for the strongest version of the 4d a-theorem, via a-maximization along RG flows, Nucl. Phys. B 702 (2004) 131 [hep-th/0408156] [INSPIRE].
M. Berkooz, The dual of supersymmetric SU(2k) with an antisymmetric tensor and composite dualities, Nucl. Phys. B 452 (1995) 513 [hep-th/9505067] [INSPIRE].
P. Pouliot, Duality in SUSY SU(N) with an antisymmetric tensor, Phys. Lett. B 367 (1996) 151 [hep-th/9510148] [INSPIRE].
M.A. Luty, M. Schmaltz and J. Terning, A sequence of duals for Sp(2N) supersymmetric gauge theories with adjoint matter, Phys. Rev. D 54 (1996) 7815 [hep-th/9603034] [INSPIRE].
K.A. Intriligator and N. Seiberg, Duality, monopoles, dyons, confinement and oblique confinement in supersymmetric SO(Nc) gauge theories, Nucl. Phys. B 444 (1995) 125 [hep-th/9503179] [INSPIRE].
A. Sagnotti, Open strings and their symmetry groups, in the proceedings of the NATO advanced summer institute on nonperturbative quantum field theory (Cargese summer institute), (1987) [hep-th/0208020] [INSPIRE].
G. Pradisi and A. Sagnotti, Open string orbifolds, Phys. Lett. B 216 (1989) 59 [INSPIRE].
M. Bianchi and A. Sagnotti, On the systematics of open string theories, Phys. Lett. B 247 (1990) 517 [INSPIRE].
M. Bianchi and A. Sagnotti, Twist symmetry and open string Wilson lines, Nucl. Phys. B 361 (1991) 519 [INSPIRE].
J. Polchinski, Dirichlet branes and Ramond-Ramond charges, Phys. Rev. Lett. 75 (1995) 4724 [hep-th/9510017] [INSPIRE].
C. Angelantonj and A. Sagnotti, Open strings, Phys. Rept. 371 (2002) 1 [Erratum ibid. 376 (2003) 407] [hep-th/0204089] [INSPIRE].
Y. Imamura, K. Kimura and M. Yamazaki, Comments on orientifold of brane tilings, Int. J. Mod. Phys. A 23 (2008) 2299 [INSPIRE].
R. Argurio et al., Dimers, orientifolds and anomalies, JHEP 02 (2021) 153 [arXiv:2009.11291] [INSPIRE].
E. García-Valdecasas, S. Meynet, A. Pasternak and V. Tatitscheff, Dimers in a bottle, JHEP 04 (2021) 274 [arXiv:2101.02670] [INSPIRE].
I. García-Etxebarria and B. Heidenreich, S-duality in N = 1 orientifold SCFTs, Fortsch. Phys. 65 (2017) 1700013 [arXiv:1612.00853] [INSPIRE].
I. Garcia-Etxebarria, B. Heidenreich and T. Wrase, New N = 1 dualities from orientifold transitions. Part I. Field theory, JHEP 10 (2013) 007 [arXiv:1210.7799] [INSPIRE].
I. García-Etxebarria, B. Heidenreich and T. Wrase, New N = 1 dualities from orientifold transitions. Part II. String theory, JHEP 10 (2013) 006 [arXiv:1307.1701] [INSPIRE].
R. Argurio, M. Bertolini, S. Meynet and A. Pasternak, On supersymmetry breaking vacua from D-branes at orientifold singularities, JHEP 12 (2019) 145 [arXiv:1909.04682] [INSPIRE].
R. Argurio et al., The octagon and the non-supersymmetric string landscape, Phys. Lett. B 815 (2021) 136153 [arXiv:2005.09671] [INSPIRE].
R. Argurio et al., Dimers, orientifolds and stability of supersymmetry breaking vacua, JHEP 01 (2021) 061 [arXiv:2007.13762] [INSPIRE].
R. Argurio et al., The octagon at large M, JHEP 11 (2022) 114 [arXiv:2207.00525] [INSPIRE].
L.E. Ibanez, F. Marchesano and R. Rabadan, Getting just the standard model at intersecting branes, JHEP 11 (2001) 002 [hep-th/0105155] [INSPIRE].
M. Wijnholt, Geometry of particle physics, Adv. Theor. Math. Phys. 13 (2009) 947 [hep-th/0703047] [INSPIRE].
M. Cicoli et al., The Standard Model quiver in de Sitter string compactifications, JHEP 08 (2021) 109 [arXiv:2106.11964] [INSPIRE].
A. Addazi and M. Bianchi, Neutron Majorana mass from exotic instantons, JHEP 12 (2014) 089 [arXiv:1407.2897] [INSPIRE].
A. Addazi and M. Bianchi, Un-oriented quiver theories for Majorana neutrons, JHEP 07 (2015) 144 [arXiv:1502.01531] [INSPIRE].
A. Addazi and M. Bianchi, Neutron Majorana mass from exotic instantons in a Pati-Salam model, JHEP 06 (2015) 012 [arXiv:1502.08041] [INSPIRE].
A. Addazi, M. Bianchi and G. Ricciardi, Exotic see-saw mechanism for neutrinos and leptogenesis in a Pati-Salam model, JHEP 02 (2016) 035 [arXiv:1510.00243] [INSPIRE].
Y. Imamura, H. Isono, K. Kimura and M. Yamazaki, Exactly marginal deformations of quiver gauge theories as seen from brane tilings, Prog. Theor. Phys. 117 (2007) 923 [hep-th/0702049] [INSPIRE].
A. Hanany, V. Jejjala, S. Ramgoolam and R.-K. Seong, Consistency and derangements in brane tilings, J. Phys. A 49 (2016) 355401 [arXiv:1512.09013] [INSPIRE].
M. Bianchi, G. Inverso, J.F. Morales and D. Ricci Pacifici, Unoriented quivers with flavour, JHEP 01 (2014) 128 [arXiv:1307.0466] [INSPIRE].
F. Manzoni, Algebro-geometrical orientifolds and IR dualities, arXiv:2211.10113 [INSPIRE].
D. Berenstein and R.G. Leigh, Discrete torsion, AdS/CFT and duality, JHEP 01 (2000) 038 [hep-th/0001055] [INSPIRE].
D. Berenstein, V. Jejjala and R.G. Leigh, Marginal and relevant deformations of N = 4 field theories and noncommutative moduli spaces of vacua, Nucl. Phys. B 589 (2000) 196 [hep-th/0005087] [INSPIRE].
G.C. Rossi, E. Sokatchev and Y.S. Stanev, New results in the deformed N = 4 SYM theory, Nucl. Phys. B 729 (2005) 581 [hep-th/0507113] [INSPIRE].
G.C. Rossi, E. Sokatchev and Y.S. Stanev, On the all-order perturbative finiteness of the deformed N = 4 SYM theory, Nucl. Phys. B 754 (2006) 329 [hep-th/0606284] [INSPIRE].
O. Lunin and J.M. Maldacena, Deforming field theories with U(1) × U(1) global symmetry and their gravity duals, JHEP 05 (2005) 033 [hep-th/0502086] [INSPIRE].
A. Ashmore, M. Petrini, E.L. Tasker and D. Waldram, Exactly marginal deformations and their supergravity duals, Phys. Rev. Lett. 128 (2022) 191601 [arXiv:2112.08375] [INSPIRE].
E.L. Tasker, From β to η: a new cohomology for deformed Sasaki-Einstein manifolds, JHEP 04 (2022) 075 [arXiv:2112.09167] [INSPIRE].
Acknowledgments
We would like to thank Riccardo Argurio for interesting discussions and comments. MF would like to thank SISSA, Trieste for hospitality during the initial stages of this work. MF and SM would like to thank the University of Milano for the warm hospitality while working on this manuscript. MF gratefully acknowledges support from the Simons Center for Geometry and Physics (workshops “5d \( \mathcal{N} \) = 1 SCFTs and Gauge Theories on Brane Webs” and “Supersymmetric Black Holes, Holography and Microstate Counting”), Stony Brook University at which some of the research for this paper was performed. The work of AA and SR is supported in part by MIUR-PRIN contract 2017CC72MK-003. The work of MB, SM and FR is partially supported by the MIUR PRIN Grant 2020KR4KN2 “String Theory as a bridge between Gauge Theories and Quantum Gravity”. The work of MF is supported in part by the Knut and Alice Wallenberg Foundation under grant KAW 2021.0170, the VR grant 2018-04438, the Olle Engkvists Stiftelse grant No. 2180108, and in part by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754496 - FELLINI.
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: 2212.03913
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
Amariti, A., Bianchi, M., Fazzi, M. et al. Multi-planarizable quivers, orientifolds, and conformal dualities. J. High Energ. Phys. 2023, 94 (2023). https://doi.org/10.1007/JHEP09(2023)094
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2023)094