Abstract
We construct novel classes of compact G2 spaces from lifting type IIA flux backgrounds with O6 planes. There exists an extension of IIA Calabi-Yau orientifolds for which some of the D6 branes (required to solve the RR tadpole) are dissolved in F2 fluxes. The backreaction of these fluxes deforms the Calabi-Yau manifold into a specific class of SU(3)-structure manifolds. The lift to M-theory again defines compact G2 manifolds, which in case of toroidal orbifolds are a twisted generalisation of the Joyce construction. This observation also allows a clear identification of the moduli space of a warped compactification with fluxes. We provide a few explicit examples, of which some can be constructed from T-dualising known IIB orientifolds with fluxes. Finally we discuss supersymmetry breaking in this context and suggest that the purely geometric picture in M-theory could provide a simpler setting to address some of the consistency issues of moduli stabilisation and de Sitter uplifting.
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References
M. Graña, Flux compactifications in string theory: a comprehensive review, Phys. Rept. 423 (2006) 91 [hep-th/0509003] [INSPIRE].
P. Koerber, Lectures on generalized complex geometry for physicists, Fortsch. Phys. 59 (2011) 169 [arXiv:1006.1536] [INSPIRE].
D. Joyce, Compact riemannian 7-manifolds with holonomy G2. I, II, J. Diff. Geom. 43 (1996) 291.
D. Joyce, Compact riemannian 7-manifolds with holonomy G2. II, J. Diff. Geom. 43 (1996) 329.
D. Joyce, Compact manifolds with special holonomy, Oxford Mathematical Monographs. Oxford University Press, Oxford U.K. ( 2000).
A. Kovalev, Twisted connected sums and special Riemannian holonomy, math/0012189.
S. Grigorian, Moduli spaces of G 2 manifolds, Rev. Math. Phys. 22 (2010) 1061 [arXiv:0911.2185] [INSPIRE].
J. Halverson and D.R. Morrison, The landscape of M-theory compactifications on seven-manifolds with G 2 holonomy, JHEP 04 (2015) 047 [arXiv:1412.4123] [INSPIRE].
A.P. Braun and S. Schäfer-Nameki, Compact, singular G 2 -holonomy manifolds and M/heterotic/F-theory duality, JHEP 04 (2018) 126 [arXiv:1708.07215] [INSPIRE].
A. Kennon, G 2 -manifolds and M-theory compactifications, arXiv:1810.12659 [INSPIRE].
S. Kachru and J. McGreevy, M theory on manifolds of G 2 holonomy and type IIA orientifolds, JHEP 06 (2001) 027 [hep-th/0103223] [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].
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, Chiral type-II orientifold constructions as M-theory on G 2 holonomy spaces, in the proceedings of the 9th International Conference on Supersymmetry and unification of fundamental interactions (SUSY01), June 11-17, Dubna, Russia (2001), hep-th/0111179 [INSPIRE].
S. Kachru, M.B. Schulz, P.K. Tripathy and S.P. Trivedi, New supersymmetric string compactifications, JHEP 03 (2003) 061 [hep-th/0211182] [INSPIRE].
M. Graña, R. Minasian, M. Petrini and A. Tomasiello, A scan for new N = 1 vacua on twisted tori, JHEP 05 (2007) 031 [hep-th/0609124] [INSPIRE].
P. Kaste, R. Minasian, M. Petrini and A. Tomasiello, Kaluza-Klein bundles and manifolds of exceptional holonomy, JHEP 09 (2002) 033 [hep-th/0206213] [INSPIRE].
P. Kaste, R. Minasian, M. Petrini and A. Tomasiello, Nontrivial RR two form field strength and SU(3) structure, Fortsch. Phys. 51 (2003) 764 [hep-th/0301063] [INSPIRE].
J. Gaillard and J. Schmude, The lift of type IIA supergravity with D6 sources: M-theory with torsion, JHEP 02 (2010) 032 [arXiv:0908.0305] [INSPIRE].
A. Fayyazuddin and T.Z. Husain, G 2 holonomy metrics and wrapped D6-branes, Phys. Rev. D 75 (2007) 065017 [hep-th/0608163] [INSPIRE].
F. Marchesano and G. Shiu, MSSM vacua from flux compactifications, Phys. Rev. D 71 (2005) 011701 [hep-th/0408059] [INSPIRE].
F. Marchesano and G. Shiu, Building MSSM flux vacua, JHEP 11 (2004) 041 [hep-th/0409132] [INSPIRE].
S.B. Giddings and A. Maharana, Dynamics of warped compactifications and the shape of the warped landscape, Phys. Rev. D 73 (2006) 126003 [hep-th/0507158] [INSPIRE].
M.R. Douglas and G. Torroba, Kinetic terms in warped compactifications, JHEP 05 (2009) 013 [arXiv:0805.3700] [INSPIRE].
G. Shiu, G. Torroba, B. Underwood and M.R. Douglas, Dynamics of Warped Flux Compactifications, JHEP 06 (2008) 024 [arXiv:0803.3068] [INSPIRE].
M.B. Schulz and E.F. Tammaro, M-theory/type IIA duality and K3 in the Gibbons-Hawking approximation, arXiv:1206.1070 [INSPIRE].
P. Koerber and D. Tsimpis, Supersymmetric sources, integrability and generalized-structure compactifications, JHEP 08 (2007) 082 [arXiv:0706.1244] [INSPIRE].
A. Hatcher, Algebraic topology, Cambridge University Press, Cambridge U.K. (2000).
F. Marchesano, D6-branes and torsion, JHEP 05 (2006) 019 [hep-th/0603210] [INSPIRE].
J.M. Maldacena, G.W. Moore and N. Seiberg, D-brane instantons and k-theory charges, JHEP 11 (2001) 062 [hep-th/0108100] [INSPIRE].
J.F.G. Cascales and A.M. Uranga, Chiral 4d string vacua with D-branes and NS-NS and RR fluxes, JHEP 05 (2003) 011 [hep-th/0303024] [INSPIRE].
D.J. Gross and M.J. Perry, Magnetic monopoles in Kaluza-Klein theories, Nucl. Phys. B 226 (1983) 29 [INSPIRE].
M.F. Atiyah and N.J. Hitchin, Low-energy scattering of nonabelian monopoles, Phys. Lett. A 107 (1985) 21 [INSPIRE].
G.W. Gibbons and N.S. Manton, Classical and quantum dynamics of BPS monopoles, Nucl. Phys. B 274 (1986) 183 [INSPIRE].
N. Seiberg and E. Witten, Gauge dynamics and compactification to three-dimensions, hep-th/9607163 [INSPIRE].
N. Seiberg, IR dynamics on branes and space-time geometry, Phys. Lett. B 384 (1996) 81 [hep-th/9606017] [INSPIRE].
L. Martucci, Warping the Kähler potential of F-theory/IIB flux compactifications, JHEP 03 (2015) 067 [arXiv:1411.2623] [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].
P. Koerber and L. Martucci, From ten to four and back again: how to generalize the geometry, JHEP 08 (2007) 059 [arXiv:0707.1038] [INSPIRE].
T.W. Grimm and J. Louis, The effective action of type IIA Calabi-Yau orientifolds, Nucl. Phys. B 718 (2005) 153 [hep-th/0412277] [INSPIRE].
R.C. Mclean, Deformations of calibrated submanifolds, Commun. Anal. Geom. 6 (1996) 705.
F. Marchesano, D. Regalado and G. Zoccarato, On D-brane moduli stabilisation, JHEP 11 (2014) 097 [arXiv:1410.0209] [INSPIRE].
P. Koerber, Stable D-branes, calibrations and generalized Calabi-Yau geometry, JHEP 08 (2005) 099 [hep-th/0506154] [INSPIRE].
L. Martucci and P. Smyth, Supersymmetric D-branes and calibrations on general N = 1 backgrounds, JHEP 11 (2005) 048 [hep-th/0507099] [INSPIRE].
L. Martucci, D-branes on general N = 1 backgrounds: Superpotentials and D-terms, JHEP 06 (2006) 033 [hep-th/0602129] [INSPIRE].
P. Koerber and L. Martucci, Deformations of calibrated D-branes in flux generalized complex manifolds, JHEP 12 (2006) 062 [hep-th/0610044] [INSPIRE].
A. Klemm and M. Mariño, Counting BPS states on the enriques Calabi-Yau, Commun. Math. Phys. 280 (2008) 27 [hep-th/0512227] [INSPIRE].
D. Joyce, Compact Riemannian 7-manifolds with holonomy G 2, J. Diff. Goem. 43 (1996) 291.
K. Dasgupta, G. Rajesh and S. Sethi, M theory, orientifolds and G-flux, JHEP 08 (1999) 023 [hep-th/9908088] [INSPIRE].
S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].
U.H. Danielsson et al., De Sitter hunting in a classical landscape, Fortsch. Phys. 59 (2011) 897 [arXiv:1103.4858] [INSPIRE].
J. Blabäck, B. Janssen, T. Van Riet and B. Vercnocke, BPS domain walls from backreacted orientifolds, JHEP 05 (2014) 040 [arXiv:1312.6125] [INSPIRE].
G. Dall’Agata and N. Prezas, Scherk-Schwarz reduction of M-theory on G 2 -manifolds with fluxes, JHEP 10 (2005) 103 [hep-th/0509052] [INSPIRE].
U. Danielsson, G. Dibitetto and A. Guarino, KK-monopoles and G-structures in M-theory/type IIA reductions, JHEP 02 (2015) 096 [arXiv:1411.0575] [INSPIRE].
J. Scherk and J.H. Schwarz, Spontaneous breaking of supersymmetry through dimensional reduction, Phys. Lett. B 82 (1979) 60.
J. Scherk and J.H. Schwarz, How to get masses from extra dimensions, Nucl. Phys. B 153 (1979) 61 [INSPIRE].
M. Graña, R. Minasian, H. Triendl and T. Van Riet, Quantization problem in Scherk-Schwarz compactifications, Phys. Rev. D 88 (2013) 085018 [arXiv:1305.0785] [INSPIRE].
E. Palti, G. Tasinato and J. Ward, WEAKLY-coupled IIA flux compactifications, JHEP 06 (2008) 084 [arXiv:0804.1248] [INSPIRE].
V. Balasubramanian, P. Berglund, J.P. Conlon and F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications, JHEP 03 (2005) 007 [hep-th/0502058] [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, De Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].
S. Sethi, Supersymmetry breaking by fluxes, JHEP 10 (2018) 022 [arXiv:1709.03554] [INSPIRE].
J. Moritz, A. Retolaza and A. Westphal, Toward de Sitter space from ten dimensions, Phys. Rev. D 97 (2018) 046010 [arXiv:1707.08678] [INSPIRE].
F.F. Gautason, V. Van Hemelryck and T. Van Riet, The tension between 10D supergravity and dS uplifts, Fortsch. Phys. 67 (2019) 1800091 [arXiv:1810.08518] [INSPIRE].
M. Larfors, D. Lüst and D. Tsimpis, Flux compactification on smooth, compact three-dimensional toric varieties, JHEP 07 (2010) 073 [arXiv:1005.2194] [INSPIRE].
M. Larfors, A. Lukas and F. Ruehle, Calabi-Yau manifolds and SU(3) structure, JHEP 01 (2019) 171 [arXiv:1805.08499] [INSPIRE].
S. Kachru and S.P. Trivedi, A comment on effective field theories of flux vacua, Fortsch. Phys. 67 (2019) 1800086 [arXiv:1808.08971] [INSPIRE].
M. Cicoli et al., De Sitter vs. quintessence in string theory, Fortsch. Phys. 67 (2019) 1800079 [arXiv:1808.08967] [INSPIRE].
J. Blåbäck et al., Smeared versus localised sources in flux compactifications, JHEP 12 (2010) 043 [arXiv:1009.1877] [INSPIRE].
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Andriolo, S., Shiu, G., Triendl, H. et al. Compact G2 holonomy spaces from SU(3) structures. J. High Energ. Phys. 2019, 59 (2019). https://doi.org/10.1007/JHEP03(2019)059
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DOI: https://doi.org/10.1007/JHEP03(2019)059