Internal circle uplifts, transversality and stratified Gstructures
Abstract
We study stratified Gstructures in ${\cal N}=2$ compactifications of Mtheory on eightmanifolds $M$ using the uplift to the auxiliary ninemanifold ${\hat M}=M\times S^1$. We show that the cosmooth generalized distribution ${\hat {\cal D}}$ on ${\hat M}$ which arises in this formalism may have pointwise transverse or nontransverse intersection with the pullback of the tangent bundle of $M$, a fact which is responsible for the subtle relation between the spinor stabilizers arising on $M$ and ${\hat M}$ and for the complicated stratified Gstructure on $M$ which we uncovered in previous work. We give a direct explanation of the latter in terms of the former and relate explicitly the defining forms of the $\mathrm{SU}(2)$ structure which exists on the generic locus ${\cal U}$ of $M$ to the defining forms of the $\mathrm{SU}(3)$ structure which exists on an open subset ${\hat {\cal U}}$ of ${\hat M}$, thus providing a dictionary between the eight and ninedimensional formalisms.
 Publication:

arXiv eprints
 Pub Date:
 May 2015
 DOI:
 10.48550/arXiv.1505.05238
 arXiv:
 arXiv:1505.05238
 Bibcode:
 2015arXiv150505238M
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Differential Geometry
 EPrint:
 24 pages