The KK-compactification of M-theory on fibers which are 8-manifolds. In the low-energy limiting 11-dimensional supergravity this is KK-compactification to 3d supergravity.
Typically this is considered with a reduction of the structure group on the compactification fiber from Spin(8) to Spin(7), in which case one speaks of M-theory on Spin(7)-manifolds (see the references below). Further reduction to G2-structure yields M-theory on G2-manifolds.
In M-theory compactified compact 8-manifold fibers, tadpole cancellation for the supergravity C-field (see also at C-field tadpole cancellation) is equivalently the condition
where
is the net number of M2-branes in the spacetime (whose worldvolume appears as points in );
is the field strength/flux of the supergravity C-field
is the first Pontryagin class and the second Pontryagin class combining to I8, all regarded here in rational homotopy theory.
If has
or
then
is the Euler class (see this Prop. and this Prop., respectively), hence in these cases the condition is equivalently
where is the Euler characteristic of .
For references see there.
If the 8-dimensional fibers themselves are elliptic fibrations, then M-theory on these 8-manifolds is supposedly T-dual to F-theory KK-compactified to spacetime-dimensions.
In particular, if there is an M2-brane filling the base 2+1-dimensional spacetime, this is supposedly T-dual to a 3+1-dimensional spacetime filling D3-brane in F-theory (e.g. Condeescu-Micu-Palti 14, p. 2)
For more on this see at F/M-theory on elliptically fibered Calabi-Yau 4-folds and at F-theory on Spin(7)-manifolds and at Witten's Dark Fantasy.
(Bonetti-Grimm-Pugh 13a, Bonetti-Grimm-Pugh 13b, reviewed in Pugh)
The discovery of exotic 7-spheres proceeded via 8-manifolds with boundary homeomorphic to the 7-sphere , but not necessarily diffeomorphic to with its canonical smooth structure (for more see there).
Hence when regarded from the point of view of M-theory on 8-manifolds, exotic 7-spheres arise as near horizon limits of peculiar black M2-brane spacetimes .
See also Morrison-Plesser 99, section 3.2.
On a spin-manifold of dimension 8 a choice of topological Spin(7)-structure is equivalently a choice of cocycle in J-twisted Cohomotopy cohomology theory. This follows (FSS 19, 3.4) from
the standard coset space-structures on the 7-sphere (see here)
the fact that coset spaces are the homotopy fibers of the maps of the corresponding classifying spaces (see here)
Edward Witten, Strong Coupling and the Cosmological Constant, Mod. Phys. Lett.A10:2153-2156, 1995 (arXiv:hep-th/9506101)
(on possible relation to the cosmological constant: Witten's Dark Fantasy)
Katrin Becker, Melanie Becker, M-Theory on Eight-Manifolds, Nucl. Phys. B477 (1996) 155-167 (arXiv:hep-th/9605053)
Savdeep Sethi, Cumrun Vafa, Edward Witten, Constraints on Low-Dimensional String Compactifications, Nucl. Phys. B480: 213-224, 1996 (arXiv:hep-th/9606122)
Discussion in terms of G-structures:
Chris Isham, Christopher Pope, Nowhere Vanishing Spinors and Topological Obstructions to the Equivalence of the NSR and GS Superstrings, Class. Quant. Grav. 5 (1988) 257 (spire:251240, doi:10.1088/0264-9381/5/2/006)
(focus on Spin(7)-structure)
Chris Isham, Christopher Pope, Nicholas Warner, Nowhere-vanishing spinors and triality rotations in 8-manifolds, Classical and Quantum Gravity, Volume 5, Number 10, 1988 (cds:185144, doi:10.1088/0264-9381/5/10/009)
(focus on Spin(7)-structure)
Cezar Condeescu, Andrei Micu, Eran Palti, M-theory Compactifications to Three Dimensions with M2-brane Potentials, JHEP 04 (2014) 026 (arXiv:1311.5901)
Daniël Prins, Dimitrios Tsimpis, IIA supergravity and M-theory on manifolds with structure, Phys. Rev. D 89.064030 (arXiv:1312.1692)
Elena Babalic, Calin Lazaroiu, Foliated eight-manifolds for M-theory compactification, JHEP 01 (2015) 140 (arXiv:1411.3148)
C. S. Shahbazi, M-theory on non-Kähler manifolds, JHEP 09 (2015) 178 (arXiv:1503.00733)
Elena Babalic, Calin Lazaroiu, Singular foliations for M-theory compactification, JHEP 03 (2015) 116 (arXiv:1411.3497)
Elena Babalic, Calin Lazaroiu, The landscape of -structures in eight-manifold compactifications of M-theory, JHEP 11 (2015) 007 (arXiv:1505.02270)
Elena Babalic, Calin Lazaroiu, Internal circle uplifts, transversality and stratified -structures, JHEP 11 (2015) 174 (arXiv:1505.05238)
Discussion of KK-compactification on 8-dimensional Spin(7)-manifolds (see also at M-theory on G2-manifolds and at F-theory on Spin(7)-manifolds):
Mirjam Cvetic, Gary Gibbons, H. Lu, Christopher Pope, New Complete Non-compact Spin(7) Manifolds, Nucl. Phys. B620: 29-54, 2002 (arXiv:hep-th/0103155)
Jaydeep Majumder, Type IIA Orientifold Limit of M-Theory on Compact Joyce 8-Manifold of Spin(7)-Holonomy, JHEP 0201 (2002) 048 (arXiv:hep-th/0109076)
Ralph Blumenhagen, Volker Braun, Superconformal Field Theories for Compact Manifolds with Spin(7) Holonomy, JHEP 0112:013, 2001 (arXiv:hep-th/0111048)
Sergei Gukov, James Sparks, M-Theory on Manifolds, Nucl. Phys. B625 (2002) 3-69 (arXiv:hep-th/0109025)
Sergei Gukov, James Sparks, David Tong, Conifold Transitions and Five-Brane Condensation in M-Theory on Manifolds, Class. Quant. Grav. 20 (2003) 665-706 [arXiv:hep-th/0207244]
Melanie Becker, Dragos Constantin, Sylvester James Gates Jr., William D. Linch III, Willie Merrell, J. Phillips, M-theory on Manifolds, Fluxes and 3D, Supergravity, Nucl. Phys. B683 (2004) 67-104 (arXiv:hep-th/0312040)
Dragos Constantin, M-Theory Vacua from Warped Compactifications on Manifolds, Nucl. Phys. B706: 221-244, 2005 (arXiv:hep-th/0410157)
Dragos Constantin, Flux Compactification of M-theory on Compact Manifolds with Holonomy, Fortsch. Phys. 53 (2005) 1272-1329 (arXiv:hep-th/0507104)
Dimitrios Tsimpis, M-theory on eight-manifolds revisited: supersymmetry and generalized structures, JHEP 0604 (2006) 027 (arXiv:hep-th/0511047)
S. Salur, O. Santillan, New holonomy metrics admiting holonomy reductions and M-theory/IIA dualities, Phys. Rev. D79: 086009, 2009 (arXiv:0811.4422)
Adil Belhaj, Luis J. Boya, Antonio Segui, Holonomy Groups Coming From F-Theory Compactification, Int J Theor Phys (2010) 49: 681. (arXiv:0911.2125)
Thomas Bruun Madsen, -manifolds with three-torus symmetry, J. Geom. Phys. 61: 2285-2292, 2011 (arXiv:1104.3089)
Federico Bonetti, Thomas Grimm, Tom Pugh, Non-Supersymmetric F-Theory Compactifications on Manifolds, JHEP 01 (2014) 112 (arXiv:1307.5858)
Federico Bonetti, Thomas Grimm, Eran Palti, Tom Pugh, F-Theory on Manifolds: Weak-Coupling Limit, JHEP02(2014)076 (arXiv:1309.2287)
Tom Pugh, M-theory on -manifolds and their F-theory duals (pdf)
Andreas Braun, Sakura Schaefer-Nameki, -Manifolds as Generalized Connected Sums and 3d Theories, JHEP 06 (2018) 103 (arXiv:1803.10755)
(generalization of compact twisted connected sum G2-manifolds)
See also
Relating M-theory on Spin(7)-manifolds with F-theory on Spin(7)-manifolds via Higgs bundles:
M-theory on HP^2, hence on a quaternion-Kähler manifold of dimension 8 with holonomy Sp(2).Sp(1), is considered in
and argued to be dual to M-theory on G2-manifolds in three different ways, which in turn is argued to lead to a possible proof of confinement in the resulting 4d effective field theory (see there for more).
See also
For more on the following see at Witten's Dark Fantasy:
An argument for non-perturbative non-supersymmetric 4d string phenomenology with fundamentally vanishing cosmological constant, based on 3d M-theory on 8-manifolds decompactified at strong coupling to 4d via duality between M-theory and type IIA string theory (recall the super 2-brane in 4d):
Edward Witten, p. 7 of: The Cosmological Constant From The Viewpoint Of String Theory, lecture at DM2000, in: David Kline (ed.) Sources and detection of dark matter and dark energy in the universe 2000, Springer 2001. 27-36. (arXiv:hep-ph/0002297, doi:10.1007/978-3-662-04587-9)
(see p. 7)
Edward Witten, Strong coupling and the cosmological constant, Mod. Phys. Lett. A 10:2153-2156, 1995 (arXiv:hep-th/9506101)
Edward Witten, Section 3 of Some Comments On String Dynamics, talk at Strings95 (arXiv:hep-th/9507121)
The realization of this scenario in F-theory on Spin(7)-manifolds:
Cumrun Vafa, Section 4.3 of: Evidence for F-Theory, Nucl. Phys. B469:403-418, 1996 (arxiv:hep-th/9602022)
Federico Bonetti, Thomas Grimm, Tom Pugh, Non-Supersymmetric F-Theory Compactifications on Manifolds, JHEP 01 (2014) 112 (arXiv:1307.5858)
Federico Bonetti, Thomas Grimm, Eran Palti, Tom Pugh, F-Theory on Manifolds: Weak-Coupling Limit, JHEP 02 (2014) 076 (arXiv:1309.2287)
Jonathan Heckman, Craig Lawrie, Ling Lin, Gianluca Zoccarato, F-theory and Dark Energy, Fortschritte der Physik (arXiv:1811.01959, doi:10.1002/prop.201900057)
Jonathan Heckman, Craig Lawrie, Ling Lin, Jeremy Sakstein, Gianluca Zoccarato, Pixelated Dark Energy (arXiv:1901.10489)
Discussion of M-theory KK-compactified on the product manifold of two K3s:
Paul Aspinwall, An Analysis of Fluxes by Duality,(arXiv:hep-th/0504036, spire:679724)
Paul Aspinwall, Renata Kallosh, Fixing All Moduli for M-Theory on , JHEP 0510:001, 2005 (arXiv:hep-th/0506014)
Andreas Braun, Arthur Hebecker, Christoph Ludeling, Roberto Valandro, Fixing D7 Brane Positions by F-Theory Fluxes, Nucl. Phys. B815:256-287, 2009 (arXiv:0811.2416)
Under duality between M-theory and type IIA string theory this translates to D6-branes wrapped on K3 (enhancon mechanism):
Review:
Satoshi Yamaguchi, Enhancon and Resolution of Singularity (arXiv:gr-qc/0108084)
Laur Järv, The enhancon mechanism in string theory, Durham 2002 (spire:899784, etheses:3981, pdf)
Last revised on January 24, 2023 at 16:41:55. See the history of this page for a list of all contributions to it.