Coulomb and Higgs branches from canonical singularities. I: Hypersurfaces with smooth Calabi-Yau resolutions. (English) Zbl 1522.81613
Summary: Compactification of M-theory and of IIB string theory on threefold canonical singularities gives rise to superconformal field theories (SCFTs) in 5d and 4d, respectively. The resolutions and deformations of the singularities encode salient features of the SCFTs and of their moduli spaces. In this paper, we build on Part 0 of this series [the authors, “Coulomb and Higgs branches from canonical singularities. Part 0”, ibid. 2021, No. 2, Paper No. 3, 58 p. (2021; doi:10.1007/JHEP02(2021)003)] and further explore the physics of SCFTs arising from isolated hypersurface singularities. We study in detail these canonical isolated hypersurface singularities that admit a smooth Calabi-Yau (crepant) resolution. Their 5d and 4d physics is discussed and their 3d reduction and mirrors (the magnetic quivers) are determined in many cases. As an explorative tool, we provide a Mathematica code which computes key quantities for any canonical isolated hypersurface singularity, including the 5d rank, the 4d Coulomb branch spectrum and central charges, higher-form symmetries in 4d and 5d, and crepant resolutions.
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81V22 | Unified quantum theories |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 83E30 | String and superstring theories in gravitational theory |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
Software:
MathematicaReferences:
| [1] | 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 |
| [2] | A. D. Shapere and C. Vafa, BPS structure of Argyres-Douglas superconformal theories, hep-th/9910182 [INSPIRE]. |
| [3] | D. Xie and S.-T. Yau, 4d N = 2 SCFT and singularity theory. Part I. Classification, arXiv:1510.01324 [INSPIRE]. |
| [4] | 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 |
| [5] | 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 |
| [6] | Closset, C.; Giacomelli, S.; Schäfer-Nameki, S.; Wang, Y-N, 5d and 4d SCFTs: canonical singularities, trinions and S-dualities, JHEP, 05, 274 (2021) · Zbl 1466.83118 · doi:10.1007/JHEP05(2021)274 |
| [7] | C. Closset, S. Schafer-Nameki and Y.-N. Wang, Coulomb and Higgs branches from canonical singularities. Part II, to appear. |
| [8] | S. S.-T. Yau and Y. Yu, Classification of 3-dimensional isolated rational hypersurface singularities with c^∗-action, Rocky Mountain J. Math.35 (2005) 1795. · Zbl 1112.14005 |
| [9] | Davenport, IC; Melnikov, IV, Landau-Ginzburg skeletons, JHEP, 05, 050 (2017) · Zbl 1380.81395 · doi:10.1007/JHEP05(2017)050 |
| [10] | Buican, M.; Jiang, H., 1-form symmetry, isolated N = 2 SCFTs, and Calabi-Yau threefolds, JHEP, 12, 024 (2021) · Zbl 1521.81378 · doi:10.1007/JHEP12(2021)024 |
| [11] | Bourget, A., The Higgs mechanism — Hasse diagrams for symplectic singularities, JHEP, 01, 157 (2020) · doi:10.1007/JHEP01(2020)157 |
| [12] | Bourget, A.; Grimminger, JF; Hanany, A.; Sperling, M.; Zhong, Z., Magnetic quivers from brane webs with O5 planes, JHEP, 07, 204 (2020) · doi:10.1007/JHEP07(2020)204 |
| [13] | Bourget, A.; Grimminger, JF; Hanany, A.; Sperling, M.; Zafrir, G.; Zhong, Z., Magnetic quivers for rank 1 theories, JHEP, 09, 189 (2020) · doi:10.1007/JHEP09(2020)189 |
| [14] | Bourget, A.; Grimminger, JF; Hanany, A.; Kalveks, R.; Sperling, M.; Zhong, Z., Magnetic lattices for orthosymplectic quivers, JHEP, 12, 092 (2020) · doi:10.1007/JHEP12(2020)092 |
| [15] | van Beest, M.; Bourget, A.; Eckhard, J.; Schäfer-Nameki, S., (Symplectic) leaves and (5d Higgs) branches in the Poly(go)nesian tropical rain forest, JHEP, 11, 124 (2020) · Zbl 1461.81132 · doi:10.1007/JHEP11(2020)124 |
| [16] | Van Beest, M.; Bourget, A.; Eckhard, J.; Schäfer-Nameki, S., (5d RG-flow) trees in the tropical rain forest, JHEP, 03, 241 (2021) · Zbl 1461.81087 · doi:10.1007/JHEP03(2021)241 |
| [17] | Akhond, M.; Carta, F.; Dwivedi, S.; Hayashi, H.; Kim, S-S; Yagi, F., Five-brane webs, Higgs branches and unitary/orthosymplectic magnetic quivers, JHEP, 12, 164 (2020) · doi:10.1007/JHEP12(2020)164 |
| [18] | A. Bourget, J. F. Grimminger, A. Hanany, M. Sperling and Z. Zhong, Branes, quivers, and the affine Grassmannian, arXiv:2102.06190 [INSPIRE]. |
| [19] | Bourget, A.; Grimminger, JF; Martone, M.; Zafrir, G., Magnetic quivers for rank 2 theories, JHEP, 03, 208 (2022) · Zbl 1522.81600 · doi:10.1007/JHEP03(2022)208 |
| [20] | A. Bourget, J. F. Grimminger, A. Hanany, R. Kalveks and Z. Zhong, Higgs branches of U/SU quivers via brane locking, arXiv:2111.04745 [INSPIRE]. |
| [21] | Akhond, M.; Carta, F.; Dwivedi, S.; Hayashi, H.; Kim, S-S; Yagi, F., Factorised 3d N = 4 orthosymplectic quivers, JHEP, 05, 269 (2021) · Zbl 1466.81073 · doi:10.1007/JHEP05(2021)269 |
| [22] | van Beest, M.; Giacomelli, S., Connecting 5d Higgs branches via Fayet-Iliopoulos deformations, JHEP, 12, 202 (2021) · Zbl 1521.81403 · doi:10.1007/JHEP12(2021)202 |
| [23] | Nawata, S.; Sperling, M.; Wang, HE; Zhong, Z., Magnetic quivers and line defects — on a duality between 3d N = 4 unitary and orthosymplectic quivers, JHEP, 02, 174 (2022) · Zbl 1522.81653 · doi:10.1007/JHEP02(2022)174 |
| [24] | M. Sperling and Z. Zhong, Balanced B and D-type orthosymplectic quivers — magnetic quivers for product theories, arXiv:2111.00026 [INSPIRE]. |
| [25] | Collinucci, A.; Valandro, R., A string theory realization of special unitary quivers in 3 dimensions, JHEP, 11, 157 (2020) · Zbl 1456.83094 · doi:10.1007/JHEP11(2020)157 |
| [26] | Collinucci, A.; De Marco, M.; Sangiovanni, A.; Valandro, R., Higgs branches of 5d rank-zero theories from geometry, JHEP, 10, 018 (2021) · doi:10.1007/JHEP10(2021)018 |
| [27] | De Marco, M.; Sangiovanni, A., Higgs branches of rank-0 5d theories from M-theory on (A_j, A_l) and (A_k, D_n) singularities, JHEP, 03, 099 (2022) · Zbl 1522.81342 · doi:10.1007/JHEP03(2022)099 |
| [28] | M. Reid et al., Canonical 3-folds, in Journees de geometrie algebrique d’Angers, Sijthoff and Noordhoff, Alphen aan den Rijn, The Netherlands (1980), p. 273. · Zbl 0451.14014 |
| [29] | V. I. Arnol’d, Critical points of smooth functions and their normal forms, Russian Math. Surv.30 (1975) 1. · Zbl 0343.58001 |
| [30] | Katz, S.; Mayr, P.; Vafa, C., Mirror symmetry and exact solution of 4D N = 2 gauge theories: 1, Adv. Theor. Math. Phys., 1, 53 (1998) · Zbl 0912.32016 · doi:10.4310/ATMP.1997.v1.n1.a2 |
| [31] | J. N. Mather and S. S.-T. Yau, Classification of isolated hypersurface singularities by their moduli algebras, Invent. Math.69 (1982) 243. · Zbl 0499.32008 |
| [32] | Shapere, AD; Tachikawa, Y., Central charges of N = 2 superconformal field theories in four dimensions, JHEP, 09, 109 (2008) · Zbl 1245.81250 · doi:10.1088/1126-6708/2008/09/109 |
| [33] | Wang, Y.; Xie, D.; Yau, SST; Yau, S-T, 4d N = 2 SCFT from complete intersection singularity, Adv. Theor. Math. Phys., 21, 801 (2017) · Zbl 1384.81139 · doi:10.4310/ATMP.2017.v21.n3.a6 |
| [34] | Caorsi, M.; Cecotti, S., Geometric classification of 4d N = 2 SCFTs, JHEP, 07, 138 (2018) · Zbl 1395.81205 · doi:10.1007/JHEP07(2018)138 |
| [35] | Argyres, PC; Martone, M., Towards a classification of rank r N = 2 SCFTs. Part II. Special Kähler stratification of the Coulomb branch, JHEP, 12, 022 (2020) · Zbl 1457.81096 · doi:10.1007/JHEP12(2020)022 |
| [36] | S. Cecotti, M. Del Zotto, M. Martone and R. Moscrop, The characteristic dimension of four-dimensional N = 2 SCFTs, arXiv:2108.10884 [INSPIRE]. |
| [37] | M. Reid et al., Minimal models of canonical 3-folds, in Algebraic varieties and analytic varieties, Mathematical Society of Japan, Japan (1983), p. 131. |
| [38] | M. Reid et al., Young person’s guide to canonical singularities, Alg. Geom. Bowdoin46 (1985) 345. · Zbl 0634.14003 |
| [39] | 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 |
| [40] | P. Jefferson, H.-C. Kim, C. Vafa and G. Zafrir, Towards classification of 5d SCFTs: single gauge node, arXiv:1705.05836 [INSPIRE]. |
| [41] | 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 |
| [42] | C. Closset and M. Del Zotto, On 5d SCFTs and their BPS quivers. Part I. B-branes and brane tilings, arXiv:1912.13502 [INSPIRE]. |
| [43] | 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 |
| [44] | Closset, C.; Magureanu, H., The U -plane of rank-one 4d N = 2 K K theories, SciPost Phys., 12, 065 (2022) · doi:10.21468/SciPostPhys.12.2.065 |
| [45] | M. Caibar, Minimal models of canonical singularities and their cohomology, Ph.D. thesis, University of Warwick, U.K. (1999). · Zbl 1082.14017 |
| [46] | M. Caibar, Minimal models of canonical 3-fold singularities and their Betti numbers, Int. Math. Res. Not.2005 (2005) 1563. · Zbl 1082.14017 |
| [47] | Batyrev, VV, Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties, J. Alg. Geom., 3, 493 (1994) · Zbl 0829.14023 |
| [48] | Lawrie, C.; Schäfer-Nameki, S., The Tate form on steroids: resolution and higher codimension fibers, JHEP, 04, 061 (2013) · Zbl 1342.81302 · doi:10.1007/JHEP04(2013)061 |
| [49] | 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 |
| [50] | Gaiotto, D.; Kapustin, A.; Seiberg, N.; Willett, B., Generalized global symmetries, JHEP, 02, 172 (2015) · Zbl 1388.83656 · doi:10.1007/JHEP02(2015)172 |
| [51] | 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 |
| [52] | Albertini, F.; Del Zotto, M.; García Etxebarria, I.; Hosseini, SS, Higher form symmetries and M-theory, JHEP, 12, 203 (2020) · Zbl 1457.81085 · doi:10.1007/JHEP12(2020)203 |
| [53] | Del Zotto, M.; García Etxebarria, I.; Hosseini, SS, Higher form symmetries of Argyres-Douglas theories, JHEP, 10, 056 (2020) · doi:10.1007/JHEP10(2020)056 |
| [54] | 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 |
| [55] | R. C. Randell, The homology of generalized Brieskorn manifolds, Topology14 (1975) 347. · Zbl 0317.57012 |
| [56] | P. Orlik, On the homology of weighted homogeneous manifolds, in Proceedings of the second conference on compact transformation groups, H.T. Ku, L.N. Mann, J.L. Sicks and J.C. Su eds., Springer, Berlin, Heidelberg, Germany (1972), p. 260. · Zbl 0249.57029 |
| [57] | Candelas, P.; de la Ossa, XC, Comments on conifolds, Nucl. Phys. B, 342, 246 (1990) · doi:10.1016/0550-3213(90)90577-Z |
| [58] | B. G. Cooper, On the monodromy at isolated singularities of weighted homogeneous polynomials, Trans. Amer. Math. Soc.269 (1982) 149. · Zbl 0487.14001 |
| [59] | Aharony, O.; Seiberg, N.; Tachikawa, Y., Reading between the lines of four-dimensional gauge theories, JHEP, 08, 115 (2013) · Zbl 1342.81248 · doi:10.1007/JHEP08(2013)115 |
| [60] | Del Zotto, M.; Heckman, JJ; Park, DS; Rudelius, T., On the defect group of a 6D SCFT, Lett. Math. Phys., 106, 765 (2016) · Zbl 1372.32034 · doi:10.1007/s11005-016-0839-5 |
| [61] | García Etxebarria, I.; Heidenreich, B.; Regalado, D., IIB flux non-commutativity and the global structure of field theories, JHEP, 10, 169 (2019) · Zbl 1427.81101 |
| [62] | Bhardwaj, L.; Hubner, M.; Schäfer-Nameki, S., 1-form symmetries of 4d N = 2 class S theories, SciPost Phys., 11, 096 (2021) · doi:10.21468/SciPostPhys.11.5.096 |
| [63] | Bhardwaj, L.; Hubner, M.; Schäfer-Nameki, S., Liberating confinement from Lagrangians: 1-form symmetries and lines in 4d N = 1 from 6d N = (2, 0), SciPost Phys., 12, 040 (2022) · doi:10.21468/SciPostPhys.12.1.040 |
| [64] | Hosseini, SS; Moscrop, R., Maruyoshi-Song flows and defect groups of \({D}_p^b(G)\) theories, JHEP, 10, 119 (2021) · doi:10.1007/JHEP10(2021)119 |
| [65] | Kreuzer, M.; Skarke, H., On the classification of quasihomogeneous functions, Commun. Math. Phys., 150, 137 (1992) · Zbl 0767.57019 · doi:10.1007/BF02096569 |
| [66] | Wolfram Research Inc., Mathematica, version 12.3.1, https://www.wolfram.com/mathematica/, U.S.A. (2021). |
| [67] | S. Cecotti, A. Neitzke and C. Vafa, R-twisting and 4d/2d correspondences, arXiv:1006.3435 [INSPIRE]. · Zbl 1355.81120 |
| [68] | Lerche, W.; Vafa, C.; Warner, NP, Chiral rings in N = 2 superconformal theories, Nucl. Phys. B, 324, 427 (1989) · doi:10.1016/0550-3213(89)90474-4 |
| [69] | S. Gukov, C. Vafa and E. Witten, CFT’s from Calabi-Yau four folds, Nucl. Phys. B584 (2000) 69 [Erratum ibid.608 (2001) 477] [hep-th/9906070] [INSPIRE]. · Zbl 0984.81143 |
| [70] | D. G. Markushevich, Canonical singularities of three-dimensional hypersurfaces, Math. U.S.S.R.-Izvestiya26 (1986) 315. · Zbl 0595.14026 |
| [71] | 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 |
| [72] | Argyres, P.; Lotito, M.; Lü, Y.; Martone, M., Geometric constraints on the space of N = 2 SCFTs. Part III. Enhanced Coulomb branches and central charges, JHEP, 02, 003 (2018) · Zbl 1387.81302 · doi:10.1007/JHEP02(2018)003 |
| [73] | Minahan, JA; Nemeschansky, D., An N = 2 superconformal fixed point with E_6global symmetry, Nucl. Phys. B, 482, 142 (1996) · Zbl 0925.81309 · doi:10.1016/S0550-3213(96)00552-4 |
| [74] | Cecotti, S.; Del Zotto, M.; Giacomelli, S., More on the N = 2 superconformal systems of type D_p(G), JHEP, 04, 153 (2013) · Zbl 1342.81564 · doi:10.1007/JHEP04(2013)153 |
| [75] | 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 |
| [76] | J. Tian and Y.-N. Wang, 5D and 6D SCFTs from C^3orbifolds, arXiv:2110.15129 [INSPIRE]. |
| [77] | D. R. Heath-Brown, The density of rational points on Cayley’s cubic surface, math.NT/0210333. · Zbl 1060.11038 |
| [78] | F. Apruzzi, C. Lawrie, L. Lin, S. Schäfer-Nameki and Y.-N. Wang, 5d superconformal field theories and graphs, Phys. Lett. B800 (2020) 135077 [arXiv:1906.11820]. · Zbl 1434.81093 |
| [79] | 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 |
| [80] | 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 |
| [81] | Di Pietro, L.; Komargodski, Z., Cardy formulae for SUSY theories in d = 4 and d = 6, JHEP, 12, 031 (2014) · Zbl 1390.81586 · doi:10.1007/JHEP12(2014)031 |
| [82] | Buican, M.; Nishinaka, T., On the superconformal index of Argyres-Douglas theories, J. Phys. A, 49 (2016) · Zbl 1342.81264 · doi:10.1088/1751-8113/49/1/015401 |
| [83] | Arabi Ardehali, A., High-temperature asymptotics of supersymmetric partition functions, JHEP, 07, 025 (2016) · Zbl 1390.81557 · doi:10.1007/JHEP07(2016)025 |
| [84] | Beem, C.; Rastelli, L., Vertex operator algebras, Higgs branches, and modular differential equations, JHEP, 08, 114 (2018) · Zbl 1396.81191 · doi:10.1007/JHEP08(2018)114 |
| [85] | Giacomelli, S., RG flows with supersymmetry enhancement and geometric engineering, JHEP, 06, 156 (2018) · Zbl 1395.81266 · doi:10.1007/JHEP06(2018)156 |
| [86] | Giacomelli, S.; Mekareeya, N.; Sacchi, M., New aspects of Argyres-Douglas theories and their dimensional reduction, JHEP, 03, 242 (2021) · Zbl 1461.81126 · doi:10.1007/JHEP03(2021)242 |
| [87] | Kang, MJ; Lawrie, C.; Song, J., Infinitely many 4D N = 2 SCFTs with a = c and beyond, Phys. Rev. D, 104 (2021) · doi:10.1103/PhysRevD.104.105005 |
| [88] | Carta, F.; Giacomelli, S.; Mekareeya, N.; Mininno, A., Conformal manifolds and 3d mirrors of (D_n, D_m) theories, JHEP, 02, 014 (2022) · Zbl 1469.81056 · doi:10.1007/JHEP02(2022)014 |
| [89] | U. Derenthal, Singular del Pezzo surfaces whose universal torsors are hypersurfaces, Proc. Lond. Math. Soc.108 (2013) 638. · Zbl 1292.14027 |
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.
