Abstract
We study six dimensional supergravity theories with superconformal sectors (SCFTs). Instances of such theories can be engineered using type IIB strings, or more generally F-Theory, which translates field theoretic constraints to geometry. Specifically, we study the fate of the discrete 2-form global symmetries of the SCFT sectors. For both (2, 0) and (1, 0) theories we show that whenever the charge lattice of the SCFT sectors is non-primitively embedded into the charge lattice of the supergravity theory, there is a subgroup of these 2-form symmetries that remains unbroken by BPS strings. By the absence of global symmetries in quantum gravity, this subgroup much be gauged. Using the embedding of the charge lattices also allows us to determine how the gauged 2-form symmetry embeds into the 2-form global symmetries of the SCFT sectors, and we present several concrete examples, as well as some general observations. As an alternative derivation, we recover our results for a large class of models from a dual perspective upon reduction to five dimensions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
W. Nahm, Supersymmetries and their Representations, Nucl. Phys. B 135 (1978) 149 [INSPIRE].
O.J. Ganor, D.R. Morrison and N. Seiberg, Branes, Calabi-Yau spaces, and toroidal compactification of the N = 1 six-dimensional E8 theory, Nucl. Phys. B 487 (1997) 93 [hep-th/9610251] [INSPIRE].
D. Gaiotto and S.S. Razamat, \( \mathcal{N} \) = 1 theories of class \( {\mathcal{S}}_k \) , JHEP 07 (2015) 073 [arXiv:1503.05159] [INSPIRE].
S.S. Razamat, C. Vafa and G. Zafrir, 4d \( \mathcal{N} \) = 1 from 6d (1, 0), JHEP 04 (2017) 064 [arXiv:1610.09178] [INSPIRE].
I. Bah, A. Hanany, K. Maruyoshi, S.S. Razamat, Y. Tachikawa and G. Zafrir, 4d \( \mathcal{N} \) = 1 from 6d \( \mathcal{N} \) = (1, 0) on a torus with fluxes, JHEP 06 (2017) 022 [arXiv:1702.04740] [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].
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].
H.-C. Kim, S.S. Razamat, C. Vafa and G. Zafrir, Compactifications of ADE conformal matter on a torus, JHEP 09 (2018) 110 [arXiv:1806.07620] [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].
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].
S.S. Razamat and E. Sabag, Sequences of 6d SCFTs on generic Riemann surfaces, JHEP 01 (2020) 086 [arXiv:1910.03603] [INSPIRE].
F. Apruzzi, C. Lawrie, L. Lin, S. Schäfer-Nameki and Y.-N. Wang, 5d Superconformal Field Theories and Graphs, Phys. Lett. B 800 (2020) 135077 [arXiv:1906.11820] [INSPIRE].
F. Apruzzi, C. Lawrie, L. Lin, S. Schäfer-Nameki and Y.-N. Wang, Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States, JHEP 11 (2019) 068 [arXiv:1907.05404] [INSPIRE].
F. Apruzzi, C. Lawrie, L. Lin, S. Schäfer-Nameki and Y.-N. Wang, Fibers add Flavor, Part II: 5d SCFTs, Gauge Theories, and Dualities, JHEP 03 (2020) 052 [arXiv:1909.09128] [INSPIRE].
F. Apruzzi, S. Schäfer-Nameki and Y.-N. Wang, 5d SCFTs from Decoupling and Gluing, JHEP 08 (2020) 153 [arXiv:1912.04264] [INSPIRE].
L. Bhardwaj and P. Jefferson, Classifying 5d SCFTs via 6d SCFTs: Rank one, JHEP 07 (2019) 178 [Addendum ibid. 01 (2020) 153] [arXiv:1809.01650] [INSPIRE].
L. Bhardwaj and P. Jefferson, Classifying 5d SCFTs via 6d SCFTs: Arbitrary rank, JHEP 10 (2019) 282 [arXiv:1811.10616] [INSPIRE].
L. Bhardwaj, On the classification of 5d SCFTs, JHEP 09 (2020) 007 [arXiv:1909.09635] [INSPIRE].
L. Bhardwaj, P. Jefferson, H.-C. Kim, H.-C. Tarazi and C. Vafa, Twisted Circle Compactifications of 6d SCFTs, JHEP 12 (2020) 151 [arXiv:1909.11666] [INSPIRE].
L. Bhardwaj, Do all 5d SCFTs descend from 6d SCFTs?, JHEP 04 (2021) 085 [arXiv:1912.00025] [INSPIRE].
F. Baume, M.J. Kang and C. Lawrie, Two 6d origins of 4d SCFTs: class S and 6d (1, 0) on a torus, arXiv:2106.11990 [INSPIRE].
E. Witten, String theory dynamics in various dimensions, Nucl. Phys. B 443 (1995) 85 [hep-th/9503124] [INSPIRE].
N. Seiberg and E. Witten, Comments on string dynamics in six-dimensions, Nucl. Phys. B 471 (1996) 121 [hep-th/9603003] [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].
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].
Y. Tachikawa, Frozen singularities in M and F-theory, JHEP 06 (2016) 128 [arXiv:1508.06679] [INSPIRE].
L. Bhardwaj, D.R. Morrison, Y. Tachikawa and A. Tomasiello, The frozen phase of F-theory, JHEP 08 (2018) 138 [arXiv:1805.09070] [INSPIRE].
L. Bhardwaj, Revisiting the classifications of 6d SCFTs and LSTs, JHEP 03 (2020) 171 [arXiv:1903.10503] [INSPIRE].
J.J. Heckman and T. Rudelius, Top Down Approach to 6D SCFTs, J. Phys. A 52 (2019) 093001 [arXiv:1805.06467] [INSPIRE].
D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, Generalized Global Symmetries, JHEP 02 (2015) 172 [arXiv:1412.5148] [INSPIRE].
M. Del Zotto, J.J. Heckman, D.S. Park and T. Rudelius, On the Defect Group of a 6D SCFT, Lett. Math. Phys. 106 (2016) 765 [arXiv:1503.04806] [INSPIRE].
F. Albertini, M. Del Zotto, I. García Etxebarria and S.S. Hosseini, Higher Form Symmetries and M-theory, JHEP 12 (2020) 203 [arXiv:2005.12831] [INSPIRE].
M. Del Zotto, I. García Etxebarria and S.S. Hosseini, Higher form symmetries of Argyres-Douglas theories, JHEP 10 (2020) 056 [arXiv:2007.15603] [INSPIRE].
L. Bhardwaj and S. Schäfer-Nameki, Higher-form symmetries of 6d and 5d theories, JHEP 02 (2021) 159 [arXiv:2008.09600] [INSPIRE].
S. Gukov, P.-S. Hsin and D. Pei, Generalized global symmetries of T [M ] theories. Part I, JHEP 04 (2021) 232 [arXiv:2010.15890] [INSPIRE].
C. Córdova, T.T. Dumitrescu and K. Intriligator, Exploring 2-Group Global Symmetries, JHEP 02 (2019) 184 [arXiv:1802.04790] [INSPIRE].
C. Delcamp and A. Tiwari, From gauge to higher gauge models of topological phases, JHEP 10 (2018) 049 [arXiv:1802.10104] [INSPIRE].
F. Benini, C. Córdova and P.-S. Hsin, On 2-Group Global Symmetries and their Anomalies, JHEP 03 (2019) 118 [arXiv:1803.09336] [INSPIRE].
C. Cordova, T.T. Dumitrescu and K. Intriligator, 2-Group Global Symmetries and Anomalies in Six-Dimensional Quantum Field Theories, JHEP 04 (2021) 252 [arXiv:2009.00138] [INSPIRE].
M. Del Zotto and K. Ohmori, 2-Group Symmetries of 6D Little String Theories and T-duality, Annales Henri Poincaré 22 (2021) 2451 [arXiv:2009.03489] [INSPIRE].
F. Apruzzi, L. Bhardwaj, J. Oh and S. Schäfer-Nameki, The Global Form of Flavor Symmetries and 2-Group Symmetries in 5d SCFTs, arXiv:2105.08724 [INSPIRE].
C. Vafa, The String landscape and the swampland, hep-th/0509212 [INSPIRE].
E. Palti, The Swampland: Introduction and Review, Fortsch. Phys. 67 (2019) 1900037 [arXiv:1903.06239] [INSPIRE].
C.W. Misner and J.A. Wheeler, Classical physics as geometry: Gravitation, electromagnetism, unquantized charge, and mass as properties of curved empty space, Annals Phys. 2 (1957) 525 [INSPIRE].
T. Banks and N. Seiberg, Symmetries and Strings in Field Theory and Gravity, Phys. Rev. D 83 (2011) 084019 [arXiv:1011.5120] [INSPIRE].
D. Harlow and H. Ooguri, Symmetries in quantum field theory and quantum gravity, Commun. Math. Phys. 383 (2021) 1669 [arXiv:1810.05338] [INSPIRE].
D. Harlow and H. Ooguri, Constraints on Symmetries from Holography, Phys. Rev. Lett. 122 (2019) 191601 [arXiv:1810.05337] [INSPIRE].
T. Banks and L.J. Dixon, Constraints on String Vacua with Space-Time Supersymmetry, Nucl. Phys. B 307 (1988) 93 [INSPIRE].
M. Del Zotto, J.J. Heckman, D.R. Morrison and D.S. Park, 6D SCFTs and Gravity, JHEP 06 (2015) 158 [arXiv:1412.6526] [INSPIRE].
N. Seiberg and W. Taylor, Charge Lattices and Consistency of 6D Supergravity, JHEP 06 (2011) 001 [arXiv:1103.0019] [INSPIRE].
M. Gross, A Finiteness theorem for elliptic Calabi-Yau threefolds, alg-geom/9305002 [INSPIRE].
A. Grassi, On minimal models of elliptic threefolds, Math. Ann. 290 (1991) 287.
H.-C. Tarazi and C. Vafa, On The Finiteness of 6d Supergravity Landscape, arXiv:2106.10839 [INSPIRE].
M.B. Green, J.H. Schwarz and P.C. West, Anomaly Free Chiral Theories in Six-Dimensions, Nucl. Phys. B 254 (1985) 327 [INSPIRE].
A. Sagnotti, A Note on the Green-Schwarz mechanism in open string theories, Phys. Lett. B 294 (1992) 196 [hep-th/9210127] [INSPIRE].
J. Tate, Algorithm for determining the type of a singular fiber in an elliptic pencil, in Modular Functions of One Variable IV, B.J. Birch and W. Kuyk eds., pp. 33–52, Springer Berlin Heidelberg, Berlin, Heidelberg (1975) [DOI].
D. Mumford, The topology of normal singularities of an algebraic surface and a criterion for simplicity, Publ. Math. Inst. Hautes Études Sci. 9 (1961) 5.
O.J. Ganor and A. Hanany, Small E8 instantons and tensionless noncritical strings, Nucl. Phys. B 474 (1996) 122 [hep-th/9602120] [INSPIRE].
D.R. Morrison and W. Taylor, Classifying bases for 6D F-theory models, Central Eur. J. Phys. 10 (2012) 1072 [arXiv:1201.1943] [INSPIRE].
M. Del Zotto, J.J. Heckman, A. Tomasiello and C. Vafa, 6d Conformal Matter, JHEP 02 (2015) 054 [arXiv:1407.6359] [INSPIRE].
M. Dierigl, P.-K. Oehlmann and F. Ruehle, Non-Simply-Connected Symmetries in 6D SCFTs, JHEP 10 (2020) 173 [arXiv:2005.12929] [INSPIRE].
L. Bhardwaj, M. Del Zotto, J.J. Heckman, D.R. Morrison, T. Rudelius and C. Vafa, F-theory and the Classification of Little Strings, Phys. Rev. D 93 (2016) 086002 [Erratum ibid. 100 (2019) 029901] [arXiv:1511.05565] [INSPIRE].
I. García Etxebarria, B. Heidenreich and D. Regalado, IIB flux non-commutativity and the global structure of field theories, JHEP 10 (2019) 169 [arXiv:1908.08027] [INSPIRE].
D.R. Morrison, S. Schäfer-Nameki and B. Willett, Higher-Form Symmetries in 5d, JHEP 09 (2020) 024 [arXiv:2005.12296] [INSPIRE].
V.V. Nikulin, Integer symmetric bilinear forms and some of their geometric applications, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979) 111.
Y. Tachikawa, On the 6d origin of discrete additional data of 4d gauge theories, JHEP 05 (2014) 020 [arXiv:1309.0697] [INSPIRE].
O. Aharony and E. Witten, Anti-de Sitter space and the center of the gauge group, JHEP 11 (1998) 018 [hep-th/9807205] [INSPIRE].
E. Witten, AdS/CFT correspondence and topological field theory, JHEP 12 (1998) 012 [hep-th/9812012] [INSPIRE].
E. Witten, Geometric Langlands From Six Dimensions, arXiv:0905.2720 [INSPIRE].
D.S. Freed, G.W. Moore and G. Segal, Heisenberg Groups and Noncommutative Fluxes, Annals Phys. 322 (2007) 236 [hep-th/0605200] [INSPIRE].
M. Henningson, The partition bundle of type AN−1 (2, 0) theory, JHEP 04 (2011) 090 [arXiv:1012.4299] [INSPIRE].
D.S. Freed and C. Teleman, Relative quantum field theory, Commun. Math. Phys. 326 (2014) 459 [arXiv:1212.1692] [INSPIRE].
P.S. Aspinwall, K 3 surfaces and string duality, in Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 96): Fields, Strings, and Duality, pp. 421–540 (1996) [hep-th/9611137] [INSPIRE].
P.K. Townsend, A New Anomaly Free Chiral Supergravity Theory From Compactification on K 3, Phys. Lett. B 139 (1984) 283 [INSPIRE].
A. Font, B. Fraiman, M. Graña, C.A. Núñez and H.P. De Freitas, Exploring the landscape of heterotic strings on Td, JHEP 10 (2020) 194 [arXiv:2007.10358] [INSPIRE].
H.-C. Kim, H.-C. Tarazi and C. Vafa, Four-dimensional \( \mathcal{N} \) = 4 SYM theory and the swampland, Phys. Rev. D 102 (2020) 026003 [arXiv:1912.06144] [INSPIRE].
K. Nishiyama, The jacobian fibrations on some k3 surfaces and their mordell-weil groups, Jap. J. Math. 22 (1996) 293.
M. Schütt and T. Shioda, Elliptic surfaces, Adv. Stud. Pure Math. 2010 (2010) 51.
N. Hajouji and P.-K. Oehlmann, Modular Curves and Mordell-Weil Torsion in F-theory, JHEP 04 (2020) 103 [arXiv:1910.04095] [INSPIRE].
A.P. Braun, Y. Kimura and T. Watari, On the Classification of Elliptic Fibrations modulo Isomorphism on K 3 Surfaces with large Picard Number, arXiv:1312.4421 [INSPIRE].
A. Kumar, Elliptic fibrations on a generic jacobian kummer surface, J. Alg. Geom. 23 (2014) 599.
P.S. Aspinwall and D.R. Morrison, Nonsimply connected gauge groups and rational points on elliptic curves, JHEP 07 (1998) 012 [hep-th/9805206] [INSPIRE].
C. Mayrhofer, D.R. Morrison, O. Till and T. Weigand, Mordell-Weil Torsion and the Global Structure of Gauge Groups in F-theory, JHEP 10 (2014) 016 [arXiv:1405.3656] [INSPIRE].
M. Cvetič, M. Dierigl, L. Lin and H.Y. Zhang, String Universality and Non-Simply-Connected Gauge Groups in 8d, Phys. Rev. Lett. 125 (2020) 211602 [arXiv:2008.10605] [INSPIRE].
F. Apruzzi, M. Dierigl and L. Lin, The Fate of Discrete 1-Form Symmetries in 6d, arXiv:2008.09117 [INSPIRE].
R. Miranda and U. Persson, Configurations of infibers on elliptic K3 surfaces, Math. Z. 201 (1989) 339.
I. Shimada, On elliptic K3 surfaces, math/0505140.
D. Klevers, D.K. Mayorga Pena, P.-K. Oehlmann, H. Piragua and J. Reuter, F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches, JHEP 01 (2015) 142 [arXiv:1408.4808] [INSPIRE].
P. Candelas and A. Font, Duality between the webs of heterotic and type-II vacua, Nucl. Phys. B 511 (1998) 295 [hep-th/9603170] [INSPIRE].
V. Bouchard and H. Skarke, Affine Kac-Moody algebras, CHL strings and the classification of tops, Adv. Theor. Math. Phys. 7 (2003) 205 [hep-th/0303218] [INSPIRE].
D.R. Morrison and W. Taylor, Toric bases for 6D F-theory models, Fortsch. Phys. 60 (2012) 1187 [arXiv:1204.0283] [INSPIRE].
G. Martini and W. Taylor, 6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces, JHEP 06 (2015) 061 [arXiv:1404.6300] [INSPIRE].
W. Taylor and Y.-N. Wang, Non-toric bases for elliptic Calabi-Yau threefolds and 6D F-theory vacua, Adv. Theor. Math. Phys. 21 (2017) 1063 [arXiv:1504.07689] [INSPIRE].
T. Oda, Convex bodies and algebraic geometry, Springer (1988) [http://eudml.org/doc/203658].
L.B. Anderson, X. Gao, J. Gray and S.-J. Lee, Multiple Fibrations in Calabi-Yau Geometry and String Dualities, JHEP 10 (2016) 105 [arXiv:1608.07555] [INSPIRE].
L.B. Anderson, X. Gao, J. Gray and S.-J. Lee, Fibrations in CICY Threefolds, JHEP 10 (2017) 077 [arXiv:1708.07907] [INSPIRE].
P.-K. Oehlmann, J. Reuter and T. Schimannek, Mordell-Weil Torsion in the Mirror of Multi-Sections, JHEP 12 (2016) 031 [arXiv:1604.00011] [INSPIRE].
B. Heidenreich, J. McNamara, M. Montero, M. Reece, T. Rudelius and I. Valenzuela, Non-Invertible Global Symmetries and Completeness of the Spectrum, JHEP 09 (2021) 203 [arXiv:2104.07036] [INSPIRE].
M. Cvetič, M. Dierigl, L. Lin and H.Y. Zhang, Higher-Form Symmetries and Their Anomalies in M-/F-Theory Duality, arXiv:2106.07654 [INSPIRE].
K.S. Narain, New Heterotic String Theories in Uncompactified Dimensions < 10, Phys. Lett. B 169 (1986) 41 [INSPIRE].
K.S. Narain, M.H. Sarmadi and E. Witten, A Note on Toroidal Compactification of Heterotic String Theory, Nucl. Phys. B 279 (1987) 369 [INSPIRE].
J. Conway and N. Sloane, Sphere Packings, Lattices and Groups, Grundlehren der mathematischen Wissenschaften, Springer New York (1998) [DOI].
P.-K. Oehlmann and T. Schimannek, GV-Spectroscopy for F-theory on genus-one fibrations, JHEP 09 (2020) 066 [arXiv:1912.09493] [INSPIRE].
A.-K. Kashani-Poor, Determining F-theory Matter Via Gromov-Witten Invariants, Commun. Math. Phys. 386 (2021) 1155 [arXiv:1912.10009] [INSPIRE].
A. Grassi and T. Weigand, Elliptic threefolds with high Mordell-Weil rank, arXiv:2105.02863 [INSPIRE].
R. Gopakumar and C. Vafa, M theory and topological strings. 1, hep-th/9809187 [INSPIRE].
R. Gopakumar and C. Vafa, M theory and topological strings. 2, hep-th/9812127 [INSPIRE].
T.W. Grimm and A. Kapfer, Anomaly Cancelation in Field Theory and F-theory on a Circle, JHEP 05 (2016) 102 [arXiv:1502.05398] [INSPIRE].
A. Font, B. Fraiman, M. Graña, C.A. Núñez and H. Parra De Freitas, Exploring the landscape of CHL strings on Td, arXiv:2104.07131 [INSPIRE].
B. Fraiman and H.P. De Freitas, Symmetry Enhancements in 7d Heterotic Strings, arXiv:2106.08189 [INSPIRE].
H.P.F. Swinnerton-Dyer, A Brief Guide to Algebraic Number Theory, London Mathematical Society Student Texts, Cambridge University Press (2001) [DOI].
W. Stein, Algebraic Number Theory, a Computational Approach, https://wstein.org/books/ant/ant.pdf .
F. Hirzebruch, Über vierdimensionaleRiemannsche Flächen mehrdeutiger analytischer Funktionen von zwei komplexen Veränderlichen, Math. Ann. 126 (1953) 1.
T. Oda, Torus embeddings and applications, vol. 58 of Tata Inst. Fund. Res. Lectures on Math. and Phys, Springer (1978).
W. Fulton, Introduction to toric varieties, Annals of mathematics studies, Princeton University Press, Princeton, NJ (1993) [https://cds.cern.ch/record/1436535].
M. Larfors, D. Lüst and D. Tsimpis, Flux compactification on smooth, compact three-dimensional toric varieties, JHEP 07 (2010) 073 [arXiv:1005.2194] [INSPIRE].
V.V. Batyrev, Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties, J. Alg. Geom. 3 (1994) 493 [alg-geom/9310003] [INSPIRE].
D. Cox and S. Katz, Mirror Symmetry and Algebraic Geometry, Mathematical Surveys and Monographs, American Mathematical Society (1999).
M. Kreuzer, Toric geometry and Calabi-Yau compactifications, Ukr. J. Phys. 55 (2010) 613 [hep-th/0612307] [INSPIRE].
L.B. Anderson, A. Grassi, J. Gray and P.-K. Oehlmann, F-theory on Quotient Threefolds with (2,0) Discrete Superconformal Matter, JHEP 06 (2018) 098 [arXiv:1801.08658] [INSPIRE].
L.B. Anderson, J. Gray and B. Hammack, Fibrations in Non-simply Connected Calabi-Yau Quotients, JHEP 08 (2018) 128 [arXiv:1805.05497] [INSPIRE].
L.B. Anderson, J. Gray and P.-K. Oehlmann, F-Theory on Quotients of Elliptic Calabi-Yau Threefolds, JHEP 12 (2019) 131 [arXiv:1906.11955] [INSPIRE].
A.P. Braun, C.R. Brodie and A. Lukas, Heterotic Line Bundle Models on Elliptically Fibered Calabi-Yau Three-folds, JHEP 04 (2018) 087 [arXiv:1706.07688] [INSPIRE].
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: 2106.13198
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
Braun, A.P., Larfors, M. & Oehlmann, PK. Gauged 2-form symmetries in 6D SCFTs coupled to gravity. J. High Energ. Phys. 2021, 132 (2021). https://doi.org/10.1007/JHEP12(2021)132
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2021)132