Related papers: Parallelisable Heterotic Backgrounds
We find the geometry of all supersymmetric type I backgrounds by solving the gravitino and dilatino Killing spinor equations, using the spinorial geometry technique, in all cases. The solutions of the gravitino Killing spinor equation are…
We describe the linearized supergeometry of eleven dimensional supergravity with four off-shell local supersymmetries. We start with a background Minkowski 11D, N=1 superspace, and an additional ingredient of a global, constant,…
We compute invariants of quadratic forms associated to orthogonal hypergeometric groups of degree five. This allows us to determine some commensurabilities between these groups, as well as to say when some thin groups cannot be conjugate to…
Generalized parallelizable spaces allow a unified treatment of consistent maximally supersymmetric truncations of ten- and eleven-dimensional supergravity in generalized geometry. Known examples are spheres, twisted tori and hyperboloides.…
We consider the periplectic supergroup ${\bf P} (n)$ over a ground field $\Bbbk$ of characteristic $p>2$. We show that there are four blocks of ${\bf P} (n)$ of simple supermodules $L^{\epsilon}(\lambda)$ corresponding to dominant weights…
In addition to the very good theoretical motivations for supersymmetry, there are now at least nine phenomenological indications that nature is supersymmetric. All are indirect, so more is better. They are enumerated here. Some discussion…
We construct the N=1 supergravity analog of the Green-Schwarz and heterotic superstring theories in 10D. We find the SO(8) theory previously found by compactification of 10D on $K3$. We also find eleven $G_2\times G_2$ theories, two with…
We show that the holonomy of the supercovariant connection for M-theory backgrounds with $N$ Killing spinors reduces to a subgroup of $SL(32-N,\bR)\st (\oplus^N \bR^{32-N})$. We use this to give the necessary and sufficient conditions for a…
We show that all M-theory backgrounds which admit more than 29 Killing spinors are maximally supersymmetric. In particular, we find that the supercovariant curvature of all backgrounds which preserve 30 supersymmetries, subject to field…
We study the relation of two frameworks for multiplicative homotopy theories: Presentably symmetric monoidal $\infty$-categories and combinatorial symmetric monoidal model categories. Our main theorem establishes an equivalence of their…
We obtain a rigidity result for compact three-dimensional Heterotic solitons with parallel non-trivial torsion. We show that they are either hyperbolic three-manifolds or compact quotients of the Heisenberg group equipped with a…
A supersymmetric solution to type II supergravity is constructed by superposing two hyperk\"ahlers with torsion metrics. The solution is given by a K\"aler with torsion metric with $SU(3)$ holonomy. The metric is embedded into a heterotic…
We discuss compactifications of the heterotic string in the presence of background fluxes. Specifically we consider compactifications on T^6, T^5, K3 x T^2 and K3 x S^1 for which we derive the bosonic sector of the low energy effective…
We classify and describe totally geodesic and parallel hypersurfaces for the entire class of Siklos spacetimes. A large class of minimal hypersurfaces is also described.
We say that a Lie (super)algebra is ''symmetric'' if with every root (with respect to the maximal torus) it has the opposite root of the same multiplicity. Over algebraically closed fields of positive characteristics (up to 7 or 11, enough…
Similar to the symplectic cases, there is a family of fourteen orthogonal hypergeometric groups with a maximally unipotent monodromy (cf. Table 1.1). We show that two of the fourteen orthogonal hypergeometric groups associated to the pairs…
We determine the geometry of supersymmetric heterotic string backgrounds for which all parallel spinors with respect to the connection $\hat\nabla$ with torsion $H$, the NS$\otimes$NS three-form field strength, are Killing. We find that…
We reduce CR-structures on smooth elliptic and hyperbolic manifolds of CR-codimension 2 to parallelisms thus solving the problem of global equivalence for such manifolds. The parallelism that we construct is defined on a sequence of two…
We present a superspace formulation of N=1 eleven-dimensional supergravity with no manifest local Lorentz covariance, which we call teleparallel superspace. This formulation will be of great importance, when we deal with other supergravity…
We classify parallel and totally geodesic hypersurfaces of the relevant class of G\"odel-type spacetimes, with particular regard to the homogeneous examples.