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
$N_{M2}$ is the net number of M2-branes in the spacetime (whose worldvolume appears as points in $X^{(8)}$);
$G_4$ is the field strength/flux of the supergravity C-field
$p_1$ is the first Pontryagin class and $p_2$ the second Pontryagin class combining to I8, all regarded here in rational homotopy theory.
If $X^{8}$ has
or
then
is the Euler class (see this Prop. and this Prop., respectively), hence in these cases the condition is equivalently
where $\chi[X]$ is the Euler characteristic of $X$.
For references see there.
If the 8-dimensional fibers themselves are elliptic fibrations, then M-theory on these 8-manifolds this is supposedly T-dual to F-theory KK-compactified to $3+1$ 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.
The discovery of exotic 7-spheres proceeded via 8-manifolds $X$ with boundary homeomorphic to the 7-sphere $\partial X \simeq_{homeo} S^7$, but not necessarily diffeomorphic to $S^7$ 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 $\mathbb{R}^{2,1} \times X$.
See also Morrison-Plesser 99, section 3.2.
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)
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)
Sergei Gukov, James Sparks, M-Theory on $Spin(7)$ Manifolds, Nucl.Phys. B625 (2002) 3-69 (arXiv:hep-th/0109025)
Cezar Condeescu, Andrei Micu, Eran Palti, M-theory Compactifications to Three Dimensions with M2-brane Potentials, JHEP04(2014)026 (arXiv:1311.5901)
Daniël Prins, Dimitrios Tsimpis, IIA supergravity and M-theory on manifolds with SU(4) structure, PhysRevD.89.064030 (arXiv:1312.1692)
Mariana Graña, C. S. Shahbazi, Marco Zambon, $Spin(7)$-manifolds in compactifications to four dimensions, JHEP11(2014)046 (arXiv:1405.3698)
Elena Mirela Babalic, Calin Lazaroiu, Foliated eight-manifolds for M-theory compactification, JHEP01(2015)140 (arXiv:1411.3148)
C. S. Shahbazi, M-theory on non-Kähler manifolds, JHEP09(2015)178 (arXiv:1503.00733)
Elena Mirela Babalic, Calin Lazaroiu, The landscape of G-structures in eight-manifold compactifications of M-theory, JHEP11 (2015) 007 (arXiv:1505.02270)
Elena Mirela Babalic, Calin Lazaroiu, Internal circle uplifts, transversality and stratified G-structures, JHEP11(2015)174 (arXiv:1505.05238)
Discussion of KK-compactification on 8-dimensional Spin(7)-manifolds (see also at M-theory on G2-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, David Tong, Conifold Transitions and Five-Brane Condensation in M-Theory on $Spin(7)$ Manifolds, Class.Quant.Grav.20:665-706, 2003 (arXiv:hep-th/0207244)
Melanie Becker, Dragos Constantin, Sylvester James Gates Jr., William D. Linch III, Willie Merrell, J. Phillips, M-theory on Spin(7) Manifolds, Fluxes and 3D, N=1 Supergravity, Nucl.Phys. B683 (2004) 67-104 (arXiv:hep-th/0312040)
Dragos Constantin, M-Theory Vacua from Warped Compactifications on Spin(7) Manifolds, Nucl.Phys.B706:221-244, 2005 (arXiv:hep-th/0410157)
Dragos Constantin, Flux Compactification of M-theory on Compact Manifolds with Spin(7) Holonomy, Fortsch.Phys. 53 (2005) 1272-1329 (arXiv:hep-th/0507104)
Dimitrios Tsimpis, M-theory on eight-manifolds revisited: N=1 supersymmetry and generalized $Spin(7)$ structures, JHEP 0604 (2006) 027 (arXiv:hep-th/0511047)
S. Salur, O. Santillan, New Spin(7) holonomy metrics admiting G2 holonomy reductions and M-theory/IIA dualities, Phys.Rev.D79:086009, 2009 (arXiv:0811.4422)
Thomas Bruun Madsen, Spin(7)-manifolds with three-torus symmetry, J.Geom.Phys.61:2285-2292, 2011 (arXiv:1104.3089)
Federico Bonetti, Thomas Grimm, Tom G. Pugh, Non-Supersymmetric F-Theory Compactifications on Spin(7) Manifolds, JHEP01(2014)112 (arXiv:1307.5858)
Federico Bonetti, Thomas Grimm, Eran Palti, Tom G. Pugh, F-Theory on Spin(7) Manifolds: Weak-Coupling Limit, JHEP02(2014)076 (arXiv:1309.2287)
Tom Pugh, M-theory on $Spin(7)$-manifold duals and their F-theory duals (pdf)
Andreas Braun, Sakura Schaefer-Nameki, Spin(7)-Manifolds as Generalized Connected Sums and 3d $N=1$ Theories, JHEP06(2018)103 (arXiv:1803.10755)
(generalization of compact twisted connected sum G2-manifolds)
Last revised on March 25, 2019 at 07:49:05. See the history of this page for a list of all contributions to it.