Abstract
We study the physics of globally consistent four-dimensional \( \mathcal{N} \) = 1 super-symmetric M-theory compactifications on G2 manifolds constructed via twisted connected sum; there are now perhaps fifty million examples of these manifolds. We study a rich example that exhibits U(1)3 gauge symmetry and a spectrum of massive charged particles that includes a trifundamental. Applying recent mathematical results to this example, we compute the form of membrane instanton corrections to the superpotential and spacetime topology change in a compact model; the latter include both the (non-isolated) G2 flop and conifold transitions. The conifold transition spontaneously breaks the gauge symmetry to U(1)2, and associated field theoretic computations of particle charges make correct predictions for the topology of the deformed G2 manifold. We discuss physical aspects of the abelian G2 landscape broadly, including aspects of Higgs and Coulomb branches, membrane instanton corrections, and some general aspects of topology change.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Kovalev, Twisted connected sums and special Riemannian holonomy, J. Reine Angew. Math. 565 (2003) 125 [math/0012189] [INSPIRE].
A. Kovalev and N.-H. Lee, K3 surfaces with non-symplectic involution and compact irreducible G 2 -manifolds, Math. Proc. Cambridge Philos. Soc. 151 (2011) 193 [arXiv:0810.0957].
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.
M. Haskins, H.-J. Hein and J. Nordström, Asymptotically cylindrical Calabi-Yau manifolds, to appear in J. Diff. Geom. arXiv:1212.6929.
A. Corti, M. Haskins, J. Nordström and T. Pacini, G 2 -manifolds and associative submanifolds via semi-Fano 3-folds, to appear in Duke Math. J. arXiv:1207.4470 [INSPIRE].
M. Kreuzer and H. Skarke, Complete classification of reflexive polyhedra in four-dimensions, Adv. Theor. Math. Phys. 4 (2002) 1209 [hep-th/0002240] [INSPIRE].
M. Reid, The moduli space of 3-folds with K = 0 may nevertheless be irreducible, Math. Ann. 278 (1987) 329.
J. Halverson and D.R. Morrsion, On gauge enhancement and singular limits in G 2 compactifications of M-theory, to appear.
J.A. Harvey and G.W. Moore, Superpotentials and membrane instantons, hep-th/9907026 [INSPIRE].
E. Witten, Phases of N = 2 theories in two-dimensions, Nucl. Phys. B 403 (1993) 159 [hep-th/9301042] [INSPIRE].
P.S. Aspinwall, B.R. Greene and D.R. Morrison, Multiple mirror manifolds and topology change in string theory, Phys. Lett. B 303 (1993) 249 [hep-th/9301043] [INSPIRE].
P.S. Aspinwall, B.R. Greene and D.R. Morrison, Calabi-Yau moduli space, mirror manifolds and space-time topology change in string theory, Nucl. Phys. B 416 (1994) 414 [hep-th/9309097] [INSPIRE].
B.R. Greene, D.R. Morrison and A. Strominger, Black hole condensation and the unification of string vacua, Nucl. Phys. B 451 (1995) 109 [hep-th/9504145] [INSPIRE].
K. Intriligator, H. Jockers, P. Mayr, D.R. Morrison and M.R. Plesser, Conifold Transitions in M-theory on Calabi-Yau Fourfolds with Background Fluxes, Adv. Theor. Math. Phys. 17 (2013) 601 [arXiv:1203.6662] [INSPIRE].
M. Atiyah, J.M. Maldacena and C. Vafa, An M-theory flop as a large-N duality, J. Math. Phys. 42 (2001) 3209 [hep-th/0011256] [INSPIRE].
M. Atiyah and E. Witten, M theory dynamics on a manifold of G 2 holonomy, Adv. Theor. Math. Phys. 6 (2003) 1 [hep-th/0107177] [INSPIRE].
R.L. Bryant, Metrics with exceptional holonomy, Ann. Math. 126 (1987) 525.
D. Joyce, Compact Manifolds with Special Holonomy, Oxford Mathematical Monographs, Oxford University Press, Oxford U.K. (2000).
R. Harvey and H.B. Lawson Jr., Calibrated geometries, Acta Math. 148 (1982) 47.
D.D. Joyce, Compact Riemannian 7-manifolds with holonomy G 2 . I, J. Diff. Geom. 43 (1996) 291.
D.D. Joyce, Compact Riemannian 7-manifolds with holonomy G 2 . II, J. Diff. Geom. 43 (1996) 329.
E. Witten, On flux quantization in M-theory and the effective action, J. Geom. Phys. 22 (1997) 1 [hep-th/9609122] [INSPIRE].
M. Cvetič, D. Klevers, H. Piragua and P. Song, Elliptic fibrations with rank three Mordell-Weil group: F-theory with U(1) × U(1) × U(1) gauge symmetry, JHEP 03 (2014) 021 [arXiv:1310.0463] [INSPIRE].
B.S. Acharya, On Realizing N = 1 super Yang-Mills in M-theory, hep-th/0011089 [INSPIRE].
T. Friedmann and E. Witten, Unification scale, proton decay and manifolds of G 2 holonomy, Adv. Theor. Math. Phys. 7 (2003) 577 [hep-th/0211269] [INSPIRE].
G. Papadopoulos and P.K. Townsend, Compactification of D = 11 supergravity on spaces of exceptional holonomy, Phys. Lett. B 357 (1995) 300 [hep-th/9506150] [INSPIRE].
P. Candelas and X.C. de la Ossa, Comments on conifolds, Nucl. Phys. B 342 (1990) 246 [INSPIRE].
A. Brandhuber, J. Gomis, S.S. Gubser and S. Gukov, Gauge theory at large-N and new G 2 holonomy metrics, Nucl. Phys. B 611 (2001) 179 [hep-th/0106034] [INSPIRE].
M. Cvetič, G.W. Gibbons, H. Lü and C.N. Pope, Cohomogeneity one manifolds of spin(7) and G 2 holonomy, Phys. Rev. D 65 (2002) 106004 [hep-th/0108245] [INSPIRE].
M. Cvetič, G.W. Gibbons, H. Lü and C.N. Pope, M theory conifolds, Phys. Rev. Lett. 88 (2002) 121602 [hep-th/0112098] [INSPIRE].
B.S. Acharya, M theory, Joyce orbifolds and super Yang-Mills, Adv. Theor. Math. Phys. 3 (1999) 227 [hep-th/9812205] [INSPIRE].
B.S. Acharya and S. Gukov, M theory and singularities of exceptional holonomy manifolds, Phys. Rept. 392 (2004) 121 [hep-th/0409191] [INSPIRE].
M. Cvetič, G. Shiu and A.M. Uranga, Chiral type-II orientifold constructions as M-theory on G 2 holonomy spaces, hep-th/0111179 [INSPIRE].
M. Cvetič, G. Shiu and A.M. Uranga, Chiral four-dimensional N = 1 supersymmetric type 2A orientifolds from intersecting D6 branes, Nucl. Phys. B 615 (2001) 3 [hep-th/0107166] [INSPIRE].
M. Cvetič, G. Shiu and A.M. Uranga, Three family supersymmetric standard-like models from intersecting brane worlds, Phys. Rev. Lett. 87 (2001) 201801 [hep-th/0107143] [INSPIRE].
D.L. Wilkens, Closed (s − 1)-connected (2s + 1)-manifolds, s = 3, 7, Bull. London Math. Soc. 4 (1972) 27.
D. Crowley and J. Nordström, The classification of 2-connected 7-manifolds, arXiv:1406.2226.
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, Non-Abelian Gauge Symmetry and the Higgs Mechanism in F-theory, Commun. Math. Phys. 336 (2015) 1231 [arXiv:1402.5962] [INSPIRE].
A. Grassi, J. Halverson and J.L. Shaneson, Geometry and Topology of String Junctions, arXiv:1410.6817 [INSPIRE].
E. Witten, Nonperturbative superpotentials in string theory, Nucl. Phys. B 474 (1996) 343 [hep-th/9604030] [INSPIRE].
R. Blumenhagen, M. Cvetič and T. Weigand, Spacetime instanton corrections in 4D string vacua: The Seesaw mechanism for D-brane models, Nucl. Phys. B 771 (2007) 113 [hep-th/0609191] [INSPIRE].
M. Cvetič, R. Donagi, J. Halverson and J. Marsano, On Seven-Brane Dependent Instanton Prefactors in F-theory, JHEP 11 (2012) 004 [arXiv:1209.4906] [INSPIRE].
M. Kerstan and T. Weigand, Fluxed M5-instantons in F-theory, Nucl. Phys. B 864 (2012) 597 [arXiv:1205.4720] [INSPIRE].
B.S. Acharya, K. Bobkov, G. Kane, P. Kumar and D. Vaman, An M-theory Solution to the Hierarchy Problem, Phys. Rev. Lett. 97 (2006) 191601 [hep-th/0606262] [INSPIRE].
B.S. Acharya, K. Bobkov, G.L. Kane, P. Kumar and J. Shao, Explaining the Electroweak Scale and Stabilizing Moduli in M-theory, Phys. Rev. D 76 (2007) 126010 [hep-th/0701034] [INSPIRE].
C. Beasley and E. Witten, A note on fluxes and superpotentials in M-theory compactifications on manifolds of G 2 holonomy, JHEP 07 (2002) 046 [hep-th/0203061] [INSPIRE].
B.S. Acharya, G. Kane and P. Kumar, Compactified String Theories - Generic Predictions for Particle Physics, Int. J. Mod. Phys. A 27 (2012) 1230012 [arXiv:1204.2795] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1412.4123
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Halverson, J., Morrison, D.R. The landscape of M-theory compactifications on seven-manifolds with G2 holonomy. J. High Energ. Phys. 2015, 47 (2015). https://doi.org/10.1007/JHEP04(2015)047
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2015)047