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Article overview
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Timelike duality, $M'$-theory and an exotic form of the Englert solution | | Marc Henneaux
; Arash Ranjbar
; | | Date: |
21 Jun 2017 | | Abstract: | Through timelike dualities, one can generate exotic versions of $M$-theory
with different spacetime signatures. These are the $M^*$-theory with signature
$(9,2,-)$, the $M’$-theory, with signature $(6,5,+)$ and the theories with
reversed signatures $(1,10, -)$, $(2,9, +)$ and $(5,6, -)$. In $(s,t, pm)$,
$s$ is the number of space directions, $t$ the number of time directions, and
$pm$ refers to the sign of the kinetic term of the $3$ form.
The only irreducible pseudo-riemannian manifolds admitting absolute
parallelism are, besides Lie groups, the seven-sphere $S^7 equiv SO(8)/SO(7)$
and its pseudo-riemannian version $S^{3,4} equiv SO(4,4)/SO(3,4)$. [There is
also the complexification $SO(8,mathbb{C})/SO(7, mathbb{C})$, but it is of
dimension too high for our considerations.] The seven-sphere $S^7equiv
S^{7,0}$ has been found to play an important role in $11$-dimensional
supergravity, both through the Freund-Rubin solution and the Englert solution
that uses its remarkable parallelizability to turn on non trivial internal
fluxes. The spacetime manifold is in both cases $AdS_4 imes S^7$. We show
that $S^{3,4}$ enjoys a similar role in $M’$-theory and construct the exotic
form $AdS_4 imes S^{3,4}$ of the Englert solution, with non zero internal
fluxes turned on. There is no analogous solution in $M^*$-theory. | | Source: | arXiv, 1706.6948 | | Services: | Forum | Review | PDF | Favorites | |
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