HETEROTIC SOLUTIONS WITH G_2 AND Spin(7)-STRUCTURES

We study supersymmetric solutions in 7-and 8-dimensional Abelian heterotic supergravity theories.In dimension 7, the solutions are described by G 2 with torsion equations.When a G 2 manifold has principal orbits S 3 × S 3 , the equations are reduced to ordinary differential equations with four radial functions.For these equations we obtain explicit ALC metrics with S 3 -bolt and T 1,1 -bolt singularities.In dimension 8, we study supersymmetric solutions to Spin(7) with torsion equations associated with 3-Sasakian manifolds by using a similar method to the case G 2 .