Related papers: Rolling among G_2 vacua

We consider a (mathbb{Z}_2)-equivariant flow in (mathbb{R}^{4}) with an integral of motion and a hyperbolic equilibrium with a transverse homoclinic orbit (Gamma). We provide criteria for the existence of stable and unstable invariant…

We define a measure of spectral asymmetry for G_2 and Spin(7) manifolds. We show that this invariant can be computed in terms of characteristic classes and the covariant constant form defining the G_2 or Spin(7) structure.

We determine torsion class constraints for the supergravity background produced by D6-branes wrapping special Lagrangian cycles in a Calabi-Yau 3-fold. We employ a recently introduced method which involves probing the putative background by…

We introduce a notion of moment map adapted to actions of Lie groups that preserve a closed three-form. We show existence of our multi-moment maps in many circumstances, including mild topological assumptions on the underlying manifold.…

The aim of this article is to introduce and study certain topological invariants for closed, oriented three-manifolds Y. These groups are relatively Z-graded Abelian groups associated to SpinC structures over Y. Given a genus g Heegaard…

In the presence of compact dimensions massive solutions of General Relativity may take one of several forms including the black-hole and the black-string, the simplest relevant background being R^{3+1} * S^1. It is shown how Morse theory…

We show that any group $G$ is contained in some sharply 2-transitive group $\mathcal{G}$ without a non-trivial abelian normal subgroup. This answers a long-standing open question. The involutions in the groups $\mathcal{G}$ that we…

Knots and links in 3-manifolds are studied by applying intersection invariants to singular concordances. The resulting link invariants generalize the Arf invariant, the mod 2 Sato-Levine invariants, and Milnor's triple linking numbers.…

Using the twisted partition function on R^3 x S^1, we argue that the deconfinement phase transition in pure Yang-Mills theory for all simple gauge groups is continuously connected to a quantum phase transition that can be studied in a…

In this, the second of three papers about $C_2$-equivariant complex quadrics, we calculate the equivariant ordinary cohomology of smooth symmetric quadrics graded on the representation ring of $\Pi BU(1)$ and with coefficients in the…

We study supergravity solutions corresponding to fivebranes wrapped on a three-sphere inside a G_2 holonomy manifold. By changing a parameter the solutions interpolate between a G_2 manifold X_i \cong S^3 x R^4 with flux on a three-sphere…

We prove a compactness theorem for holomorphic curves in 4-dimensional symplectizations that have embedded projections to the underlying 3-manifold. It strengthens the cylindrical case of the SFT compactness theorem by using intersection…

We study the continuation of periodic orbits from various compound of homoclinics in classical system. Together with the homoclinics, the periodic orbits make up a $C^1$-smooth, normally hyperbolic invariant cylinder with holes. It plays a…

We reduce M-theory on a G_2 orbifold with co-dimension four singularities, taking explicitly into account the additional gauge fields at the singularities. As a starting point, we use 11-dimensional supergravity coupled to seven-dimensional…

We describe the infinitesimal moduli space of pairs $(Y, V)$ where $Y$ is a manifold with $G_2$ holonomy, and $V$ is a vector bundle on $Y$ with an instanton connection. These structures arise in connection to the moduli space of heterotic…

We present a systematic method for constructing manifolds with Lorentzian holonomy group that are non-static supersymmetric vacua admitting covariantly constant light-like spinors. It is based on the metric of their Riemannian counterparts…

Let $X$ be a differentiable manifold endowed with a transitive action $\alpha:A\times X\longrightarrow X$ of a Lie group $A$. Let $K$ be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms…

M-theory compactified on $G_2$-holonomy manifolds results in 4d $\mathcal{N}=1$ supersymmetric gauge theories coupled to gravity. In this paper we focus on the gauge sector of such compactifications by studying the Higgs bundle obtained…

We construct a compact manifold with a closed $G_2$ structure not admitting any torsion-free $G_2$ structure, which is non-formal and has first Betti number $b_1=1$. We develop a method of resolution for orbifolds that arise as a quotient…

On a supersymmetric sigma model the covariantly constant forms are related to the conserved currents that are generators of a super W-algebra extending the superconformal algebra. The existence of covariantly constant forms restricts the…