BPS equations and nontrivial compactifications
Abstract
We consider the problem of finding exact, elevendimensional, BPS supergravity solutions in which the compactification involves a nontrivial CalabiYau manifold, Y , as opposed to simply a T ^{6}. Since there are no explicitlyknown metrics on nontrivial, compact CalabiYau manifolds, we use a noncompact "local model" and take the compactification manifold to be Y={M}_{GH}× {T}^2 , where ℳ_{GH} is a hyperKähler, GibbonsHawking ALE space. We focus on backgrounds with three electric charges in five dimensions and find exact families of solutions to the BPS equations that have the same four supersymmetries as the threecharge black hole. Our exact solution to the BPS system requires that the CalabiYau manifold be fibered over the spacetime using compensators on Y . The role of the compensators is to ensure smoothness of the elevendimensional metric when the moduli of Y depend on the spacetime. The Maxwell field Ansatz also implicitly involves the compensators through the frames of the fibration. We examine the equations of motion and discuss the brane distributions on generic internal manifolds that do not have enough symmetry to allow smearing.
 Publication:

Journal of High Energy Physics
 Pub Date:
 May 2018
 DOI:
 10.1007/JHEP05(2018)022
 arXiv:
 arXiv:1710.06439
 Bibcode:
 2018JHEP...05..022T
 Keywords:

 Flux compactifications;
 MTheory;
 Supergravity Models;
 Black Holes in String Theory;
 High Energy Physics  Theory
 EPrint:
 32 pages, no figures