Related papers: Heterotic Solutions with G2 and Spin(7) Structures

We solve the Killing-Yano equation on manifolds with a $G$-structure for $G=SO(n), U(n), SU(n), Sp(n)\cdot Sp(1), Sp(n), G_2$ and $Spin(7)$. Solutions include nearly-K\"ahler, weak holonomy $G_2$, balanced SU(n) and holonomy $G$ manifolds.…

Metrics of exceptional holonomy are vacuum solutions to the Einstein equation. In this paper we describe manifolds with holonomy contained in Spin(7) preserved by a three-torus symmetry in terms of tri-symplectic geometry of four-manifolds.…

The usual supermembrane solution of $D=11$ supergravity interpolates between $R^{11}$ and $AdS_4 \times round~S^7$, has symmetry $P_3 \times SO(8)$ and preserves $1/2$ of the spacetime supersymmetries for either orientation of the round…

We extend the refined G-structure classification of supersymmetric solutions of eleven dimensional supergravity. We derive necessary and sufficient conditions for the existence of an arbitrary number of Killing spinors whose common isotropy…

We study supersymmetric AdS_4 x X_7 solutions of 11-dim supergravity where the tri-Sasakian space X_7 has generically U(1)^2\times SU(2)_R isometry. The compact and regular 7-dim spaces X_7=S(t_1,t_2,t_3) is originated from 8-dim…

We classify 7-dimensional cocalibrated $\G_2$-manifolds with parallel characteristic torsion and non-abelian holonomy. All these spaces admit a metric connection $\nabla^{\mathrm{c}}$ with totally skew-symmetric torsion and a spinor field…

We construct $AdS_3\times Y_7$ solutions of type IIB supergravity, where $Y_7$ is a smooth $S^5$ bundle over a spindle $\Sigma(n_N,n_S)$, which are dual to $\mathcal{N}=(0,2)$ SCFTs in $d=2$. The solutions are constructed using the $D=5$…

We first make a Killing spinor analysis for a general three-dimensional off-shell $N=(2,0)$ supergravity and find conditions for a bosonic background to preserve some supersymmetry . We then consider a particular model, namely $N=(2,0)$…

Among the possible superalgebras that contain the AdS$_3$ isometries, two interesting possibilities are the exceptional $F(4)$ and $G(3)$. Their R-symmetry is respectively SO(7) and $G_2$, and the amount of supersymmetry ${\cal N}=8$ and…

In this note, we construct new solutions to the heterotic $\mathrm{G}_2$-system with non-abelian gauge group, both compact and non-compact, on certain $2$-step nilmanifolds and $3$-Sasakian manifolds. Our approach is based on an ansatz that…

We show that the supersymmetric near horizon geometry of heterotic black holes is either an AdS_3 fibration over a 7-dimensional manifold which admits a G_2 structure compatible with a connection with skew-symmetric torsion, or it is a…

We consider some infinitesmal and global deformations of G_2 structures on 7-manifolds. We discover a canonical way to deform a G_2 structure by a vector field in which the associated metric gets "twisted" in some way by the vector cross…

We establish a general analytic and geometric framework for resolving Spin(7)--orbifolds. These spaces arise naturally as boundary points in the moduli space of exceptional holonomy metrics, and smooth Gromov--Hausdorff resolutions can be…

We investigate the $Spin(7)$ holonomy metric of cohomogeneity one with the principal orbit $SU(3)/U(1)$. A choice of U(1) in the two dimensional Cartan subalgebra is left as free and this allows manifest $\Sigma_3=W(SU(3))$ (= the Weyl…

We compactify the ten-dimensional spacetime in heterotic supergravity leaving four-dimensional Minkowski spacetime. We search for nonsupersymmetric, non-Ricci-flat solutions of the equations of motion with the quadratic curvature term. By…

Necessary and sufficient conditions to the existence of a hermitian connection with totally skew-symmetric torsion and holonomy contained in SU(3) are given. Non-compact solution to the supergravity-type I equations of motion with non-zero…

A family of geometries on S^7 arise as solutions of the classical equations of motion in 11 dimensions. In addition to the conventional riemannian geometry and the two exceptional Cartan-Schouten compact flat geometries with torsion, one…

We analyse the geometrical structure of supersymmetric solutions of type II supergravity of the form R^{1,9-n} x M_n with non-trivial NS flux and dilaton. Solutions of this type arise naturally as the near-horizon limits of wrapped NS…

We study complete, simply-connected manifolds with special holonomy that are toric with respect to their multi-moment maps. We consider the cases where there is a connected non-Abelian symmetry group containing the torus. For…

We classify the geometries of the most general warped, flux AdS backgrounds of heterotic supergravity up to two loop order in sigma model perturbation theory. We show under some mild assumptions that there are no $AdS_n$ backgrounds with…