Abstract
We study four-dimensional superconformal field theories living on the worldvolume of D3 branes probing minimally-supersymmetric F-theory backgrounds, focusing on the case of orbi-orientifold setups with and without 7-branes. We observe that these theories are closely related to compactifications of six-dimensional 𝒩 = (1, 0) theories on a torus with flux, where the flux quanta is mapped in Type IIB to the defining data of the orbifold group. We analyze the cases of class 𝒮k theories as well as of compactifications of the E-string and of orbi-instanton theories. We also classify 𝒮-fold configurations in F-theory preserving minimal supersymmetry in four dimensions and their mass deformations.
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References
N. Seiberg, Electric-magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [INSPIRE].
K.A. Intriligator and N. Seiberg, Mirror symmetry in three-dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [INSPIRE].
N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation, and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19 [hep-th/9407087] [INSPIRE].
N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484 [hep-th/9408099] [INSPIRE].
P.C. Argyres and M.R. Douglas, New phenomena in SU(3) supersymmetric gauge theory, Nucl. Phys. B 448 (1995) 93 [hep-th/9505062] [INSPIRE].
P.C. Argyres, M.R. Plesser, N. Seiberg and E. Witten, New N = 2 superconformal field theories in four-dimensions, Nucl. Phys. B 461 (1996) 71 [hep-th/9511154] [INSPIRE].
S.H. Katz, A. Klemm and C. Vafa, Geometric engineering of quantum field theories, Nucl. Phys. B 497 (1997) 173 [hep-th/9609239] [INSPIRE].
A.D. Shapere and C. Vafa, BPS structure of Argyres-Douglas superconformal theories, hep-th/9910182 [INSPIRE].
A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230] [INSPIRE].
E. Witten, Solutions of four-dimensional field theories via M theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166] [INSPIRE].
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
P.C. Argyres, J.J. Heckman, K. Intriligator and M. Martone, Snowmass White Paper on SCFTs, arXiv:2202.07683 [INSPIRE].
I. García-Etxebarria and D. Regalado, 𝒩 = 3 four dimensional field theories, JHEP 03 (2016) 083 [arXiv:1512.06434] [INSPIRE].
I. García-Etxebarria and D. Regalado, Exceptional 𝒩 = 3 theories, JHEP 12 (2017) 042 [arXiv:1611.05769] [INSPIRE].
O. Aharony, Y. Tachikawa and K. Gomi, S-folds and 4d N = 3 superconformal field theories, JHEP 06 (2016) 044 [arXiv:1602.08638] [INSPIRE].
F. Apruzzi, S. Giacomelli and S. Schäfer-Nameki, 4d 𝒩 = 2 S-folds, Phys. Rev. D 101 (2020) 106008 [arXiv:2001.00533] [INSPIRE].
S. Giacomelli, C. Meneghelli and W. Peelaers, New 𝒩 = 2 superconformal field theories from 𝒮-folds, JHEP 01 (2021) 022 [arXiv:2007.00647] [INSPIRE].
S. Giacomelli, M. Martone, Y. Tachikawa and G. Zafrir, More on 𝒩 = 2 S-folds, JHEP 01 (2021) 054 [arXiv:2010.03943] [INSPIRE].
A. Bourget et al., S-fold magnetic quivers, JHEP 02 (2021) 054 [arXiv:2010.05889] [INSPIRE].
J.J. Heckman et al., S-folds, string junctions, and 𝒩 = 2 SCFTs, Phys. Rev. D 103 (2021) 086013 [arXiv:2009.10090] [INSPIRE].
F. Apruzzi, M. Fazzi, D. Rosa and A. Tomasiello, All AdS7 solutions of type II supergravity, JHEP 04 (2014) 064 [arXiv:1309.2949] [INSPIRE].
J.J. Heckman, D.R. Morrison and C. Vafa, On the Classification of 6D SCFTs and Generalized ADE Orbifolds, JHEP 05 (2014) 028 [Erratum ibid. 06 (2015) 017] [arXiv:1312.5746] [INSPIRE].
M. Del Zotto, J.J. Heckman, A. Tomasiello and C. Vafa, 6d Conformal Matter, JHEP 02 (2015) 054 [arXiv:1407.6359] [INSPIRE].
D. Gaiotto and A. Tomasiello, Holography for (1, 0) theories in six dimensions, JHEP 12 (2014) 003 [arXiv:1404.0711] [INSPIRE].
L. Bhardwaj, Classification of 6d 𝒩 = (1, 0) gauge theories, JHEP 11 (2015) 002 [arXiv:1502.06594] [INSPIRE].
J.J. Heckman, D.R. Morrison, T. Rudelius and C. Vafa, Atomic Classification of 6D SCFTs, Fortsch. Phys. 63 (2015) 468 [arXiv:1502.05405] [INSPIRE].
L. Bhardwaj et al., F-theory and the Classification of Little Strings, Phys. Rev. D 93 (2016) 086002 [Erratum ibid. 100 (2019) 029901] [arXiv:1511.05565] [INSPIRE].
K. Ohmori, Y. Tachikawa and G. Zafrir, Compactifications of 6d N = (1, 0) SCFTs with non-trivial Stiefel-Whitney classes, JHEP 04 (2019) 006 [arXiv:1812.04637] [INSPIRE].
J.J. Heckman et al., 6D SCFTs, center-flavor symmetries, and Stiefel-Whitney compactifications, Phys. Rev. D 106 (2022) 066003 [arXiv:2205.03411] [INSPIRE].
P. Horava and E. Witten, Eleven-dimensional supergravity on a manifold with boundary, Nucl. Phys. B 475 (1996) 94 [hep-th/9603142] [INSPIRE].
D. Gaiotto and S.S. Razamat, 𝒩 = 1 theories of class 𝒮k, JHEP 07 (2015) 073 [arXiv:1503.05159] [INSPIRE].
I. Coman, E. Pomoni, M. Taki and F. Yagi, Spectral curves of 𝒩 = 1 theories of class 𝒮k, JHEP 06 (2017) 136 [arXiv:1512.06079] [INSPIRE].
S.S. Razamat, C. Vafa and G. Zafrir, 4d 𝒩 = 1 from 6d (1, 0), JHEP 04 (2017) 064 [arXiv:1610.09178] [INSPIRE].
H.-C. Kim, S.S. Razamat, C. Vafa and G. Zafrir, E-String Theory on Riemann Surfaces, Fortsch. Phys. 66 (2018) 1700074 [arXiv:1709.02496] [INSPIRE].
I. Bah et al., 4d 𝒩 = 1 from 6d 𝒩 = (1, 0) on a torus with fluxes, JHEP 06 (2017) 022 [arXiv:1702.04740] [INSPIRE].
T. Bourton and E. Pomoni, Instanton counting in class 𝒮k, J. Phys. A 53 (2020) 165401 [arXiv:1712.01288] [INSPIRE].
H.-C. Kim, S.S. Razamat, C. Vafa and G. Zafrir, D-type Conformal Matter and SU/USp Quivers, JHEP 06 (2018) 058 [arXiv:1802.00620] [INSPIRE].
F. Apruzzi, J.J. Heckman, D.R. Morrison and L. Tizzano, 4D Gauge Theories with Conformal Matter, JHEP 09 (2018) 088 [arXiv:1803.00582] [INSPIRE].
S.S. Razamat and G. Zafrir, Compactification of 6d minimal SCFTs on Riemann surfaces, Phys. Rev. D 98 (2018) 066006 [arXiv:1806.09196] [INSPIRE].
S.S. Razamat, O. Sela and G. Zafrir, Curious patterns of IR symmetry enhancement, JHEP 10 (2018) 163 [arXiv:1809.00541] [INSPIRE].
S.S. Razamat, Flavored surface defects in 4d 𝒩 = 1 SCFTs, Lett. Math. Phys. 109 (2019) 1377 [arXiv:1808.09509] [INSPIRE].
G. Zafrir, On the torus compactifications of Z2 orbifolds of E-string theories, JHEP 10 (2019) 040 [arXiv:1809.04260] [INSPIRE].
S.S. Razamat and G. Zafrir, N = 1 conformal dualities, JHEP 09 (2019) 046 [arXiv:1906.05088] [INSPIRE].
S.S. Razamat, E. Sabag and G. Zafrir, From 6d flows to 4d flows, JHEP 12 (2019) 108 [arXiv:1907.04870] [INSPIRE].
S.S. Razamat and E. Sabag, Sequences of 6d SCFTs on generic Riemann surfaces, JHEP 01 (2020) 086 [arXiv:1910.03603] [INSPIRE].
S. Pasquetti, S.S. Razamat, M. Sacchi and G. Zafrir, Rank Q E-string on a torus with flux, SciPost Phys. 8 (2020) 014 [arXiv:1908.03278] [INSPIRE].
I. Bah and F. Bonetti, Anomaly Inflow, Accidental Symmetry, and Spontaneous Symmetry Breaking, JHEP 01 (2020) 117 [arXiv:1910.07549] [INSPIRE].
I. Bah, F. Bonetti, R. Minasian and P. Weck, Anomaly Inflow Methods for SCFT Constructions in Type IIB, JHEP 02 (2021) 116 [arXiv:2002.10466] [INSPIRE].
I. Bah, F. Bonetti and R. Minasian, Discrete and higher-form symmetries in SCFTs from wrapped M5-branes, JHEP 03 (2021) 196 [arXiv:2007.15003] [INSPIRE].
I. Bah, F. Bonetti, E. Leung and P. Weck, M5-branes probing flux backgrounds, JHEP 10 (2022) 122 [arXiv:2111.01790] [INSPIRE].
T. Bourton, E. Pomoni and X. Zhang, 𝒩 = 1 Curves on Generalized Coulomb Branches of Supersymmetric Gauge Theories, Universe 8 (2022) 101 [arXiv:2111.14543] [INSPIRE].
S.S. Razamat and E. Sabag, SQCD and pairs of pants, JHEP 09 (2020) 028 [arXiv:2006.03480] [INSPIRE].
C. Hwang, S.S. Razamat, E. Sabag and M. Sacchi, Rank Q E-string on spheres with flux, SciPost Phys. 11 (2021) 044 [arXiv:2103.09149] [INSPIRE].
B. Nazzal, A. Nedelin and S.S. Razamat, Minimal (D, D) conformal matter and generalizations of the van Diejen model, SciPost Phys. 12 (2022) 140 [arXiv:2106.08335] [INSPIRE].
S.S. Razamat, E. Sabag, O. Sela and G. Zafrir, Aspects of 4d supersymmetric dynamics and geometry, arXiv:2203.06880 [INSPIRE].
I. Bah, F. Bonetti, E. Leung and P. Weck, The geometry of decoupling fields, JHEP 09 (2022) 197 [arXiv:2112.07796] [INSPIRE].
I. Bah et al., A Panorama Of Physical Mathematics c. 2022, arXiv:2211.04467 [INSPIRE].
H.-C. Kim and S.S. Razamat, Star Shaped Quivers in Four Dimensions, Phys. Rev. Lett. 130 (2023) 211601 [arXiv:2302.05113] [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].
G. Bonelli, S. Giacomelli, K. Maruyoshi and A. Tanzini, N = 1 Geometries via M-theory, JHEP 10 (2013) 227 [arXiv:1307.7703] [INSPIRE].
D. Xie, M5 brane and four dimensional N = 1 theories I, JHEP 04 (2014) 154 [arXiv:1307.5877] [INSPIRE].
S. Giacomelli, M. Moleti and R. Savelli, Probing 7-branes on orbifolds, JHEP 08 (2022) 163 [arXiv:2205.08578] [INSPIRE].
C. Beasley, J.J. Heckman and C. Vafa, GUTs and Exceptional Branes in F-theory — I, JHEP 01 (2009) 058 [arXiv:0802.3391] [INSPIRE].
M. Bianchi, D. Bufalini, S. Mancani and F. Riccioni, Mass deformations of unoriented quiver theories, JHEP 07 (2020) 015 [arXiv:2003.09620] [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].
S. Franco et al., Dimers and orientifolds, JHEP 09 (2007) 075 [arXiv:0707.0298] [INSPIRE].
I. García-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].
M. Bianchi, G. Inverso, J.F. Morales and D. Ricci Pacifici, Unoriented Quivers with Flavour, JHEP 01 (2014) 128 [arXiv:1307.0466] [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].
I. García-Etxebarria and B. Heidenreich, Strongly coupled phases of 𝒩 = 1 S-duality, JHEP 09 (2015) 032 [arXiv:1506.03090] [INSPIRE].
I. García-Etxebarria and B. Heidenreich, S-duality in 𝒩 = 1 orientifold SCFTs, Fortsch. Phys. 65 (2017) 1700013 [arXiv:1612.00853] [INSPIRE].
G. Aldazabal, L.E. Ibanez, F. Quevedo and A.M. Uranga, D-branes at singularities: A Bottom up approach to the string embedding of the standard model, JHEP 08 (2000) 002 [hep-th/0005067] [INSPIRE].
S. Franco et al., Brane dimers and quiver gauge theories, JHEP 01 (2006) 096 [hep-th/0504110] [INSPIRE].
A.M. Uranga, D-brane probes, RR tadpole cancellation and K-theory charge, Nucl. Phys. B 598 (2001) 225 [hep-th/0011048] [INSPIRE].
M. Bianchi and J.F. Morales, Anomalies \& tadpoles, JHEP 03 (2000) 030 [hep-th/0002149] [INSPIRE].
L.E. Ibanez, R. Rabadan and A.M. Uranga, Anomalous U(1)’s in type I and type IIB D = 4, N = 1 string vacua, Nucl. Phys. B 542 (1999) 112 [hep-th/9808139] [INSPIRE].
J. Park, R. Rabadan and A.M. Uranga, N = 1 type IIA brane configurations, chirality and T duality, Nucl. Phys. B 570 (2000) 3 [hep-th/9907074] [INSPIRE].
L.E. Bottini, C. Hwang, S. Pasquetti and M. Sacchi, 4d S-duality wall and SL(2, ℤ) relations, JHEP 03 (2022) 035 [arXiv:2110.08001] [INSPIRE].
C. Hwang, S. Pasquetti and M. Sacchi, Rethinking mirror symmetry as a local duality on fields, Phys. Rev. D 106 (2022) 105014 [arXiv:2110.11362] [INSPIRE].
R. Comi et al., The SL(2, ℤ) dualization algorithm at work, JHEP 06 (2023) 119 [arXiv:2212.10571] [INSPIRE].
B. Feng, Y.-H. He, A. Karch and A.M. Uranga, Orientifold dual for stuck NS5-branes, JHEP 06 (2001) 065 [hep-th/0103177] [INSPIRE].
R. Blumenhagen, L. Gorlich and B. Kors, Supersymmetric orientifolds in 6-D with D-branes at angles, Nucl. Phys. B 569 (2000) 209 [hep-th/9908130] [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].
N. Mekareeya, K. Ohmori, Y. Tachikawa and G. Zafrir, E8 instantons on type-A ALE spaces and supersymmetric field theories, JHEP 09 (2017) 144 [arXiv:1707.04370] [INSPIRE].
Y. Kimura, Four-dimensional N = 1 theories, S-fold constraints on T-branes, and behaviors in IR and UV, JHEP 05 (2021) 016 [arXiv:2011.04460] [INSPIRE].
Acknowledgments
We would like to thank Massimo Bianchi, Federico Bonetti, Sara Pasquetti, and Angel Uranga for helpful discussions. RS would like to thank the Department of Physics of the University of Milan Bicocca for kind hospitality in the final stage of this project. The work of SG is supported by the INFN grant “Per attività di formazione per sostenere progetti di ricerca” (GRANT 73/STRONGQFT).
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Giacomelli, S., Savelli, R. 𝒩 = 1 SCFTs from F-theory on Orbifolds. J. High Energ. Phys. 2023, 129 (2023). https://doi.org/10.1007/JHEP08(2023)129
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DOI: https://doi.org/10.1007/JHEP08(2023)129