Editing G2 manifold (section)

== Connections to physics ==
These manifolds are important in [[string theory]]. They break the original [[supersymmetry]] to 1/8 of the original amount. For example, [[M-theory]] compactified on a <math>G_2</math> manifold leads to a realistic four-dimensional (11-7=4) theory with N=1 supersymmetry.  The resulting low energy effective [[supergravity]] contains a single supergravity [[supermultiplet]], a number of [[chiral supermultiplet]]s equal to the third [[Betti number]] of the <math>G_2</math> manifold and a number of U(1) [[vector supermultiplet]]s equal to the second Betti number. Recently it was shown that almost contact structures (constructed by [[Sema Salur]] et al.)<ref name="arikanetal" /> play an important role in <math>G_2</math> geometry".<ref>{{citation
 | last1 = de la Ossa | first1 = Xenia | author1-link = Xenia de la Ossa
 | last2 = Larfors | first2 = Magdalena
 | last3 = Magill | first3 = Matthew
 | arxiv = 2101.12605
 | doi = 10.4310/atmp.2022.v26.n1.a3
 | issue = 1
 | journal = [[Advances in Theoretical and Mathematical Physics]]
 | mr = 4504848
 | pages = 143–215
 | title = Almost contact structures on manifolds with a {{math|''G''<sub>2</sub>}} structure
 | volume = 26
 | year = 2022}}</ref>