×

Flavor symmetry of \(5d\) SCFTs. Part I. General setup. (English) Zbl 1472.81216

Summary: A large class of \(5d\) superconformal field theories (SCFTs) can be constructed by integrating out BPS particles from \(6d\) SCFTs compactified on a circle. We describe a general method for extracting the flavor symmetry of any \(5d\) SCFT lying in this class. For this purpose, we utilize the geometric engineering of \(5d \) \(\mathcal{N} = 1\) theories in M-theory, where the flavor symmetry is encoded in a collection of non-compact surfaces.

MSC:

81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T60 Supersymmetric field theories in quantum mechanics
83E30 String and superstring theories in gravitational theory

References:

[1] Morrison, DR; Seiberg, N., Extremal transitions and five-dimensional supersymmetric field theories, Nucl. Phys. B, 483, 229 (1997) · Zbl 0925.81228 · doi:10.1016/S0550-3213(96)00592-5
[2] Intriligator, KA; Morrison, DR; Seiberg, N., Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces, Nucl. Phys. B, 497, 56 (1997) · Zbl 0934.81061 · doi:10.1016/S0550-3213(97)00279-4
[3] Diaconescu, D-E; Entin, R., Calabi-Yau spaces and five-dimensional field theories with exceptional gauge symmetry, Nucl. Phys. B, 538, 451 (1999) · Zbl 0948.81626 · doi:10.1016/S0550-3213(98)00689-0
[4] Del Zotto, M.; Heckman, JJ; Morrison, DR, 6D SCFTs and Phases of 5D Theories, JHEP, 09, 147 (2017) · Zbl 1382.81176 · doi:10.1007/JHEP09(2017)147
[5] Xie, D.; Yau, S-T, Three dimensional canonical singularity and five dimensional \(\mathcal{N} = 1\) SCFT, JHEP, 06, 134 (2017) · Zbl 1380.81416 · doi:10.1007/JHEP06(2017)134
[6] Closset, C.; Del Zotto, M.; Saxena, V., Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective, SciPost Phys., 6, 052 (2019) · doi:10.21468/SciPostPhys.6.5.052
[7] Jefferson, P.; Katz, S.; Kim, H-C; Vafa, C., On Geometric Classification of 5d SCFTs, JHEP, 04, 103 (2018) · Zbl 1390.81603 · doi:10.1007/JHEP04(2018)103
[8] Apruzzi, F.; Lin, L.; Mayrhofer, C., Phases of 5d SCFTs from M-/F-theory on Non-Flat Fibrations, JHEP, 05, 187 (2019) · Zbl 1416.81177 · doi:10.1007/JHEP05(2019)187
[9] L. Bhardwaj and P. Jefferson, Classifying 5d SCFTs via 6d SCFTs: Rank one, JHEP07 (2019) 178 [Addendum ibid.01 (2020) 153] [arXiv:1809.01650] [INSPIRE]. · Zbl 1418.81086
[10] Bhardwaj, L.; Jefferson, P., Classifying 5d SCFTs via 6d SCFTs: Arbitrary rank, JHEP, 10, 282 (2019) · Zbl 1427.81097 · doi:10.1007/JHEP10(2019)282
[11] Bhardwaj, L.; Jefferson, P.; Kim, H-C; Tarazi, H-C; Vafa, C., Twisted Circle Compactifications of 6d SCFTs, JHEP, 12, 151 (2020) · Zbl 1457.81098 · doi:10.1007/JHEP12(2020)151
[12] Apruzzi, F.; Lawrie, C.; Lin, L.; Schäfer-Nameki, S.; Wang, Y-N, 5d Superconformal Field Theories and Graphs, Phys. Lett. B, 800, 135077 (2020) · Zbl 1434.81093 · doi:10.1016/j.physletb.2019.135077
[13] Apruzzi, F.; Lawrie, C.; Lin, L.; Schäfer-Nameki, S.; Wang, Y-N, Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States, JHEP, 11, 068 (2019) · Zbl 1429.81066 · doi:10.1007/JHEP11(2019)068
[14] Apruzzi, F.; Lawrie, C.; Lin, L.; Schäfer-Nameki, S.; Wang, Y-N, Fibers add Flavor, Part II: 5d SCFTs, Gauge Theories, and Dualities, JHEP, 03, 052 (2020) · Zbl 1435.81177 · doi:10.1007/JHEP03(2020)052
[15] Bhardwaj, L., On the classification of 5d SCFTs, JHEP, 09, 007 (2020) · Zbl 1454.81179 · doi:10.1007/JHEP09(2020)007
[16] Saxena, V., Rank-two 5d SCFTs from M-theory at isolated toric singularities: a systematic study, JHEP, 04, 198 (2020) · Zbl 1436.81121 · doi:10.1007/JHEP04(2020)198
[17] Bhardwaj, L., Do all 5d SCFTs descend from 6d SCFTs?, JHEP, 04, 085 (2021) · Zbl 1462.81187 · doi:10.1007/JHEP04(2021)085
[18] Apruzzi, F.; Schäfer-Nameki, S.; Wang, Y-N, 5d SCFTs from Decoupling and Gluing, JHEP, 08, 153 (2020) · Zbl 1454.81175 · doi:10.1007/JHEP08(2020)153
[19] Bhardwaj, L.; Zafrir, G., Classification of 5d \(\mathcal{N} = 1\) gauge theories, JHEP, 12, 099 (2020) · Zbl 1457.81117 · doi:10.1007/JHEP12(2020)099
[20] Eckhard, J.; Schäfer-Nameki, S.; Wang, Y-N, Trifectas for T_Nin 5d, JHEP, 07, 199 (2020) · Zbl 1451.83090 · doi:10.1007/JHEP07(2020)199
[21] Closset, C.; Schäfer-Nameki, S.; Wang, Y-N, Coulomb and Higgs Branches from Canonical Singularities: Part 0, JHEP, 02, 003 (2021) · doi:10.1007/JHEP02(2021)003
[22] Hubner, M., 5d SCFTs from (E_n, E_m) conformal matter, JHEP, 12, 014 (2020) · Zbl 1457.81101 · doi:10.1007/JHEP12(2020)014
[23] L. Bhardwaj, More 5d KK theories, arXiv:2005.01722 [INSPIRE]. · Zbl 1461.83066
[24] Seiberg, N., Five-dimensional SUSY field theories, nontrivial fixed points and string dynamics, Phys. Lett. B, 388, 753 (1996) · doi:10.1016/S0370-2693(96)01215-4
[25] Aharony, O.; Hanany, A., Branes, superpotentials and superconformal fixed points, Nucl. Phys. B, 504, 239 (1997) · Zbl 0979.81591 · doi:10.1016/S0550-3213(97)00472-0
[26] Aharony, O.; Hanany, A.; Kol, B., Webs of (p, q) five-branes, five-dimensional field theories and grid diagrams, JHEP, 01, 002 (1998) · doi:10.1088/1126-6708/1998/01/002
[27] DeWolfe, O.; Hanany, A.; Iqbal, A.; Katz, E., Five-branes, seven-branes and five-dimensional E_nfield theories, JHEP, 03, 006 (1999) · Zbl 0965.81091 · doi:10.1088/1126-6708/1999/03/006
[28] Brandhuber, A.; Oz, Y., The D4-D8 brane system and five-dimensional fixed points, Phys. Lett. B, 460, 307 (1999) · Zbl 0987.81590 · doi:10.1016/S0370-2693(99)00763-7
[29] Bergman, O.; Rodríguez-Gómez, D.; Zafrir, G., 5-Brane Webs, Symmetry Enhancement, and Duality in 5d Supersymmetric Gauge Theory, JHEP, 03, 112 (2014) · doi:10.1007/JHEP03(2014)112
[30] Zafrir, G., Duality and enhancement of symmetry in 5d gauge theories, JHEP, 12, 116 (2014) · doi:10.1007/JHEP12(2014)116
[31] Zafrir, G., Brane webs and O5-planes, JHEP, 03, 109 (2016) · Zbl 1388.83626 · doi:10.1007/JHEP03(2016)109
[32] Hayashi, H.; Kim, S-S; Lee, K.; Yagi, F., 6d SCFTs, 5d Dualities and Tao Web Diagrams, JHEP, 05, 203 (2019) · Zbl 1416.81189 · doi:10.1007/JHEP05(2019)203
[33] Hayashi, H.; Kim, S-S; Lee, K.; Taki, M.; Yagi, F., A new 5d description of 6d D-type minimal conformal matter, JHEP, 08, 097 (2015) · Zbl 1388.81326 · doi:10.1007/JHEP08(2015)097
[34] Bergman, O.; Zafrir, G., 5d fixed points from brane webs and O7-planes, JHEP, 12, 163 (2015) · Zbl 1388.81772
[35] Hayashi, H.; Kim, S-S; Lee, K.; Yagi, F., Dualities and 5-brane webs for 5d rank 2 SCFTs, JHEP, 12, 016 (2018) · Zbl 1405.81101 · doi:10.1007/JHEP12(2018)016
[36] Hayashi, H.; Kim, S-S; Lee, K.; Yagi, F., 5-brane webs for 5d \(\mathcal{N} = 1\) G_2gauge theories, JHEP, 03, 125 (2018) · Zbl 1388.81543 · doi:10.1007/JHEP03(2018)125
[37] Hayashi, H.; Kim, S-S; Lee, K.; Yagi, F., Rank-3 antisymmetric matter on 5-brane webs, JHEP, 05, 133 (2019) · Zbl 1416.81129 · doi:10.1007/JHEP05(2019)133
[38] Witten, E., Phase transitions in M-theory and F-theory, Nucl. Phys. B, 471, 195 (1996) · Zbl 1003.81537 · doi:10.1016/0550-3213(96)00212-X
[39] Kim, H-C; Kim, S-S; Lee, K., 5-dim Superconformal Index with Enhanced En Global Symmetry, JHEP, 10, 142 (2012) · Zbl 1397.81382 · doi:10.1007/JHEP10(2012)142
[40] Zafrir, G., Brane webs, 5d gauge theories and 6d \(\mathcal{N} \) = (1, 0) SCFT’s, JHEP, 12, 157 (2015) · Zbl 1388.81370
[41] Hayashi, H.; Kim, S-S; Lee, K.; Taki, M.; Yagi, F., More on 5d descriptions of 6d SCFTs, JHEP, 10, 126 (2016) · Zbl 1390.81438 · doi:10.1007/JHEP10(2016)126
[42] Kim, S-S; Taki, M.; Yagi, F., Tao Probing the End of the World, PTEP, 2015 (2015) · Zbl 1348.81373
[43] Ohmori, K.; Shimizu, H.; Tachikawa, Y.; Yonekura, K., 6d \(\mathcal{N} \) = (1, 0) theories on S^1/T^2and class S theories: part II, JHEP, 12, 131 (2015)
[44] Yonekura, K., Instanton operators and symmetry enhancement in 5d supersymmetric quiver gauge theories, JHEP, 07, 167 (2015) · Zbl 1388.81160 · doi:10.1007/JHEP07(2015)167
[45] Zafrir, G., Instanton operators and symmetry enhancement in 5d supersymmetric USp, SO and exceptional gauge theories, JHEP, 07, 087 (2015) · Zbl 1388.81900 · doi:10.1007/JHEP07(2015)087
[46] Tachikawa, Y., Instanton operators and symmetry enhancement in 5d supersymmetric gauge theories, PTEP, 2015 (2015)
[47] Hayashi, H.; Kim, S-S; Lee, K.; Yagi, F., Equivalence of several descriptions for 6d SCFT, JHEP, 01, 093 (2017) · Zbl 1373.83105 · doi:10.1007/JHEP01(2017)093
[48] Ohmori, K.; Shimizu, H., S^1/T^2compactifications of 6d \(\mathcal{N} \) = (1, 0) theories and brane webs, JHEP, 03, 024 (2016) · Zbl 1388.81592 · doi:10.1007/JHEP03(2016)024
[49] P. Jefferson, H.-C. Kim, C. Vafa and G. Zafrir, Towards Classification of 5d SCFTs: Single Gauge Node, arXiv:1705.05836 [INSPIRE].
[50] Mekareeya, N.; Ohmori, K.; Tachikawa, Y.; Zafrir, G., E_8instantons on type-A ALE spaces and supersymmetric field theories, JHEP, 09, 144 (2017) · Zbl 1382.81207 · doi:10.1007/JHEP09(2017)144
[51] Ashok, SK, Surface operators in 5d gauge theories and duality relations, JHEP, 05, 046 (2018) · Zbl 1391.81185 · doi:10.1007/JHEP05(2018)046
[52] Bastian, B.; Hohenegger, S.; Iqbal, A.; Rey, S-J, Five-Dimensional Gauge Theories from Shifted Web Diagrams, Phys. Rev. D, 99 (2019) · doi:10.1103/PhysRevD.99.046012
[53] Assel, B.; Sciarappa, A., Wilson loops in 5d \(\mathcal{N} = 1\) theories and S-duality, JHEP, 10, 082 (2018) · Zbl 1402.81207 · doi:10.1007/JHEP10(2018)082
[54] Bhardwaj, L., Dualities of 5d gauge theories from S-duality, JHEP, 07, 012 (2020) · Zbl 1451.81323 · doi:10.1007/JHEP07(2020)012
[55] C. Closset and M. Del Zotto, On 5d SCFTs and their BPS quivers. Part I: B-branes and brane tilings, arXiv:1912.13502 [INSPIRE].
[56] Hayashi, H.; Kim, S-S; Lee, K.; Yagi, F., Complete prepotential for 5d \(\mathcal{N} = 1\) superconformal field theories, JHEP, 02, 074 (2020) · Zbl 1435.81219 · doi:10.1007/JHEP02(2020)074
[57] Morrison, DR; Schäfer-Nameki, S.; Willett, B., Higher-Form Symmetries in 5d, JHEP, 09, 024 (2020) · Zbl 1454.81231 · doi:10.1007/JHEP09(2020)024
[58] Bhardwaj, L.; Schäfer-Nameki, S., Higher-form symmetries of 6d and 5d theories, JHEP, 02, 159 (2021) · Zbl 1460.81076 · doi:10.1007/JHEP02(2021)159
[59] Benetti Genolini, P.; Tizzano, L., Instantons, symmetries and anomalies in five dimensions, JHEP, 04, 188 (2021) · Zbl 1462.81141 · doi:10.1007/JHEP04(2021)188
[60] Bergman, O.; Rodríguez-Gómez, D., 5d quivers and their AdS_6duals, JHEP, 07, 171 (2012) · Zbl 1397.83127 · doi:10.1007/JHEP07(2012)171
[61] D’Hoker, E.; Gutperle, M.; Karch, A.; Uhlemann, CF, Warped AdS_6× S^2in Type IIB supergravity I: Local solutions, JHEP, 08, 046 (2016) · Zbl 1390.83390 · doi:10.1007/JHEP08(2016)046
[62] D’Hoker, E.; Gutperle, M.; Uhlemann, CF, Holographic duals for five-dimensional superconformal quantum field theories, Phys. Rev. Lett., 118, 101601 (2017) · doi:10.1103/PhysRevLett.118.101601
[63] D’Hoker, E.; Gutperle, M.; Uhlemann, CF, Warped AdS_6× S^2in Type IIB supergravity II: Global solutions and five-brane webs, JHEP, 05, 131 (2017) · Zbl 1380.83282 · doi:10.1007/JHEP05(2017)131
[64] D’Hoker, E.; Gutperle, M.; Uhlemann, CF, Warped AdS_6× S^2in Type IIB supergravity III: Global solutions with seven-branes, JHEP, 11, 200 (2017) · Zbl 1383.83202 · doi:10.1007/JHEP11(2017)200
[65] Chaney, A.; Uhlemann, CF, On minimal Type IIB AdS_6solutions with commuting 7-branes, JHEP, 12, 110 (2018) · Zbl 1405.83071 · doi:10.1007/JHEP12(2018)110
[66] Bah, I.; Passias, A.; Weck, P., Holographic duals of five-dimensional SCFTs on a Riemann surface, JHEP, 01, 058 (2019) · Zbl 1409.81093 · doi:10.1007/JHEP01(2019)058
[67] Uhlemann, CF, Exact results for 5d SCFTs of long quiver type, JHEP, 11, 072 (2019) · Zbl 1429.81078 · doi:10.1007/JHEP11(2019)072
[68] Uhlemann, CF, AdS_6/CFT_5with O7-planes, JHEP, 04, 113 (2020) · Zbl 1436.81141 · doi:10.1007/JHEP04(2020)113
[69] L. Bhardwaj, Flavor symmetry of 5d SCFTs. Part II. Applications, JHEP04 (2021) 221 [arXiv:2010.13235] [INSPIRE].
[70] Bhardwaj, L.; Tachikawa, Y., On finite symmetries and their gauging in two dimensions, JHEP, 03, 189 (2018) · Zbl 1388.81707 · doi:10.1007/JHEP03(2018)189
[71] Douglas, MR; Katz, SH; Vafa, C., Small instantons, Del Pezzo surfaces and type I′ theory, Nucl. Phys. B, 497, 155 (1997) · Zbl 0935.81057 · doi:10.1016/S0550-3213(97)00281-2
[72] Bertolini, M.; Merkx, PR; Morrison, DR, On the global symmetries of 6D superconformal field theories, JHEP, 07, 005 (2016) · Zbl 1388.81774 · doi:10.1007/JHEP07(2016)005
[73] Merkx, PR, Classifying Global Symmetries of 6D SCFTs, JHEP, 03, 163 (2018) · Zbl 1388.81864 · doi:10.1007/JHEP03(2018)163
[74] Del Zotto, M.; Lockhart, G., Universal Features of BPS Strings in Six-dimensional SCFTs, JHEP, 08, 173 (2018) · Zbl 1396.81173 · doi:10.1007/JHEP08(2018)173
[75] Heckman, JJ; Morrison, DR; Rudelius, T.; Vafa, C., Atomic Classification of 6D SCFTs, Fortsch. Phys., 63, 468 (2015) · Zbl 1338.81326 · doi:10.1002/prop.201500024
[76] Bhardwaj, L., Revisiting the classifications of 6d SCFTs and LSTs, JHEP, 03, 171 (2020) · Zbl 1435.83170 · doi:10.1007/JHEP03(2020)171
[77] Bhardwaj, L., Classification of 6d \(\mathcal{N} \) = (1, 0) gauge theories, JHEP, 11, 002 (2015) · Zbl 1388.81285 · doi:10.1007/JHEP11(2015)002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.