Abstract
We study electric-magnetic duality in compactifications of M-theory on twisted connected sum (TCS) G2 manifolds via duality with F-theory. Specifically, we study the physics of the D3-branes in F-theory compactified on a Calabi-Yau fourfold Y, dual to a compactification of M-theory on a TCS G2 manifold X. \( \mathcal{N} \) = 2 supersymmetry is restored in an appropriate geometric limit. In that limit, we demonstrate that the dual of D3-branes probing seven-branes corresponds to the shrinking of certain surfaces and curves, yielding light particles that may carry both electric and magnetic charges. We provide evidence that the Minahan-Nemeschansky theories with En flavor symmetry may be realized in this way. The SL(2, ℤ) monodromy of the 3/7-brane system is dual to a Fourier-Mukai transform of the dual IIA/M-theory geometry in this limit, and we extrapolate this monodromy action to the global compactification. Away from the limit, the theory is broken to \( \mathcal{N} \) = 1 supersymmetry by a D-term.
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B.S. Acharya, M theory, Joyce orbifolds and superYang-Mills, Adv. Theor. Math. Phys. 3 (1999) 227 [hep-th/9812205] [INSPIRE].
B.S. Acharya, On Realizing N = 1 superYang-Mills in M theory, hep-th/0011089 [INSPIRE].
E. Witten, Anomaly cancellation on G2 manifolds, hep-th/0108165 [INSPIRE].
B.S. Acharya and E. Witten, Chiral fermions from manifolds of G2 holonomy, hep-th/0109152 [INSPIRE].
B.S. Acharya and S. Gukov, M theory and singularities of exceptional holonomy manifolds, Phys. Rept. 392 (2004) 121 [hep-th/0409191] [INSPIRE].
C. Vafa, Evidence for F theory, Nucl. Phys. B 469 (1996) 403 [hep-th/9602022] [INSPIRE].
D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds. I, Nucl. Phys. B 473 (1996) 74 [hep-th/9602114] [INSPIRE].
D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds. II, Nucl. Phys. B 476 (1996) 437 [hep-th/9603161] [INSPIRE].
T. Weigand, F-theory, PoS TASI2017 (2018) 016 [arXiv:1806.01854] [INSPIRE].
A.P. Braun, M-Theory and Orientifolds, JHEP 09 (2020) 065 [arXiv:1912.06072] [INSPIRE].
J. Halverson and D.R. Morrison, On gauge enhancement and singular limits in G2 compactifications of M-theory, JHEP 04 (2016) 100 [arXiv:1507.05965] [INSPIRE].
A. Kovalev, Twisted connected sums and special Riemannian holonomy, math/0012189 [INSPIRE].
A. Corti, M. Haskins, J. Nordström and T. Pacini, Asymptotically cylindrical Calabi–Yau 3–folds from weak Fano 3–folds, Geom. Topol. 17 (2013) 1955.
A. Corti, M. Haskins, J. Nordström and T. Pacini, G2-manifolds and associative submanifolds via semi-Fano 3-folds, Duke Math. J. 164 (2015) 1971 [arXiv:1207.4470] [INSPIRE].
J. Halverson and D.R. Morrison, The landscape of M-theory compactifications on seven-manifolds with G2 holonomy, JHEP 04 (2015) 047 [arXiv:1412.4123] [INSPIRE].
T.C. da C. Guio, H. Jockers, A. Klemm and H.-Y. Yeh, Effective Action from M-Theory on Twisted Connected Sum G2-Manifolds, Commun. Math. Phys. 359 (2018) 535 [arXiv:1702.05435] [INSPIRE].
A.P. Braun et al., Infinitely many M2-instanton corrections to M-theory on G2-manifolds, JHEP 09 (2018) 077 [arXiv:1803.02343] [INSPIRE].
A.P. Braun and S. Schäfer-Nameki, Compact, Singular G2-Holonomy Manifolds and M/Heterotic/F-Theory Duality, JHEP 04 (2018) 126 [arXiv:1708.07215] [INSPIRE].
Y. Yamada and S.-K. Yang, Affine seven-brane backgrounds and five-dimensional EN theories on S1, Nucl. Phys. B 566 (2000) 642 [hep-th/9907134] [INSPIRE].
C. Lawrie and S. Schäfer-Nameki, The Tate Form on Steroids: Resolution and Higher Codimension Fibers, JHEP 04 (2013) 061 [arXiv:1212.2949] [INSPIRE].
P. Jefferson, S. Katz, H.-C. Kim and C. Vafa, On Geometric Classification of 5d SCFTs, JHEP 04 (2018) 103 [arXiv:1801.04036] [INSPIRE].
F. Apruzzi et al., Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States, JHEP 11 (2019) 068 [arXiv:1907.05404] [INSPIRE].
K.A. Intriligator, D.R. Morrison and N. Seiberg, Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces, Nucl. Phys. B 497 (1997) 56 [hep-th/9702198] [INSPIRE].
D.R. Morrison and N. Seiberg, Extremal transitions and five-dimensional supersymmetric field theories, Nucl. Phys. B 483 (1997) 229 [hep-th/9609070] [INSPIRE].
T. Hauer and A. Iqbal, Del Pezzo surfaces and affine seven-brane backgrounds, JHEP 01 (2000) 043 [hep-th/9910054] [INSPIRE].
K. Mohri, Y. Ohtake and S.-K. Yang, Duality between string junctions and D-branes on Del Pezzo surfaces, Nucl. Phys. B 595 (2001) 138 [hep-th/0007243] [INSPIRE].
K. Hori, A. Iqbal and C. Vafa, D-branes and mirror symmetry, hep-th/0005247.
C. Closset and H. Magureanu, The U -plane of rank-one 4d \( \mathcal{N} \) = 2 KK theories, SciPost Phys. 12 (2022) 065 [arXiv:2107.03509] [INSPIRE].
N. Cabo Bizet, A. Klemm and D. Vieira Lopes, Landscaping with fluxes and the E8 Yukawa Point in F-theory, arXiv:1404.7645 [INSPIRE].
R. Friedman, J. Morgan and E. Witten, Vector bundles and F theory, Commun. Math. Phys. 187 (1997) 679 [hep-th/9701162] [INSPIRE].
P.S. Aspinwall and D.R. Morrison, Point-like instantons on K3 orbifolds, Nucl. Phys. B 503 (1997) 533 [hep-th/9705104] [INSPIRE].
S. Kondo, Type ii degenerations of k3 surfaces, Nagoya Math. J. 99 (1985) 11.
M.R. Douglas, S.H. Katz and C. Vafa, Small instantons, Del Pezzo surfaces and type I-prime theory, Nucl. Phys. B 497 (1997) 155 [hep-th/9609071] [INSPIRE].
A. Braun, D3-branes in G2, unpublished.
C. Long, A. Sheshmani, C. Vafa and S.-T. Yau, Non-Holomorphic Cycles and Non-BPS Black Branes, arXiv:2104.06420 [https://doi.org/10.1007/s00220-022-04587-4] [INSPIRE].
M. Noguchi, S. Terashima and S.-K. Yang, N = 2 superconformal field theory with ADE global symmetry on a D3-brane probe, Nucl. Phys. B 556 (1999) 115 [hep-th/9903215] [INSPIRE].
N. Seiberg, Five-dimensional SUSY field theories, nontrivial fixed points and string dynamics, Phys. Lett. B 388 (1996) 753 [hep-th/9608111] [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].
M. Martone and G. Zafrir, On the compactification of 5d theories to 4d, JHEP 08 (2021) 017 [arXiv:2106.00686] [INSPIRE].
W. Lerche, P. Mayr and N.P. Warner, Noncritical strings, Del Pezzo singularities and Seiberg-Witten curves, Nucl. Phys. B 499 (1997) 125 [hep-th/9612085] [INSPIRE].
E. Witten, Phase transitions in M-theory and F-theory, Nucl. Phys. B 471 (1996) 195 [hep-th/9603150] [INSPIRE].
J. Distler, M. Martone and A. Neitzke, On the BPS Spectrum of the Rank-1 Minahan-Nemeschansky Theories, JHEP 02 (2020) 100 [arXiv:1901.09929] [INSPIRE].
A. Harder and A. Thompson, Pseudolattices, del Pezzo surfaces, and Lefschetz fibrations, Transactions of the American Mathematical Society 373 (2019) 2071.
A. Grassi, J. Halverson and J.L. Shaneson, Matter From Geometry Without Resolution, JHEP 10 (2013) 205 [arXiv:1306.1832] [INSPIRE].
A. Grassi, J. Halverson and J.L. Shaneson, Geometry and Topology of String Junctions, arXiv:1410.6817 [INSPIRE].
A. Grassi, J. Halverson and J.L. Shaneson, Non-Abelian Gauge Symmetry and the Higgs Mechanism in F-theory, Commun. Math. Phys. 336 (2015) 1231 [arXiv:1402.5962] [INSPIRE].
A. Grassi et al., Non-simply-laced Symmetry Algebras in F-theory on Singular Spaces, JHEP 09 (2018) 129 [arXiv:1805.06949] [INSPIRE].
A. Grassi, J. Halverson, F. Ruehle and J.L. Shaneson, Dualities of deformed \( \mathcal{N} \) = 2 SCFTs from link monodromy on D3-brane states, JHEP 09 (2017) 135 [arXiv:1611.01154] [INSPIRE].
A. Grassi et al., 6D anomaly-free matter spectrum in F-theory on singular spaces, JHEP 08 (2022) 182 [arXiv:2110.06943] [INSPIRE].
D. Gaiotto, Lectures on N = 2 gauge theory, Class. Quant. Grav. 27 (2010) 214002 [INSPIRE].
A. Strominger, Yukawa Couplings in Superstring Compactification, Phys. Rev. Lett. 55 (1985) 2547 [INSPIRE].
J.J. Heckman and C. Vafa, An Exceptional Sector for F-theory GUTs, Phys. Rev. D 83 (2011) 026006 [arXiv:1006.5459] [INSPIRE].
C. Closset, S. Schäfer-Nameki and Y.-N. Wang, Coulomb and Higgs Branches from Canonical Singularities: Part 0, JHEP 02 (2021) 003 [arXiv:2007.15600] [INSPIRE].
M. Martone, Testing our understanding of scfts: a catalogue of rank-2 \( \mathcal{N} \) = 2 theories in four dimensions, JHEP 07 (2022) 123 [arXiv:2102.02443].
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Halverson, J., Sung, B. & Tian, J. Electric-magnetic duality in a class of G2-compactifications of M-theory. J. High Energ. Phys. 2023, 89 (2023). https://doi.org/10.1007/JHEP04(2023)089
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DOI: https://doi.org/10.1007/JHEP04(2023)089