Related papers: Current progress on $G_2$--instantons over twisted…

Calculations of the number of curves on a Calabi-Yau manifold via an instanton expansion do not always agree with what one would expect naively. It is explained how to account for continuous families of instantons via deformation theory and…

We give a new construction of compact Riemannian 7-manifolds with holonomy $G_2$. Let $M$ be a torsion-free $G_2$-manifold (which can have holonomy a proper subgroup of $G_2$) such that $M$ admits an involution $\iota$ preserving the…

We present a construction of closed 7-manifolds of holonomy G_2, which generalises Kovalev's twisted connected sums by taking quotients of the pieces in the construction before gluing. This makes it possible to realise a wider range of…

Using instanton homology with coefficients in $Z/2$ we construct a homomorphism $q_2$ from the homology cobordism group in dimension 3 to the integers which is not a rational linear combination of the instanton $h$--invariant and the…

We study the moduli space of $G_2$-instantons on (projectively) flat bundles over torsion-free $G_2$-orbifolds. We prove that the moduli space is compact and smooth at the irreducible locus after adding small and generic holonomy…

We present a unified eight-dimensional approach to instanton equations on several seven-dimensional manifolds associated to a six-dimensional homogeneous nearly K\"ahler manifold. The cone over the sine-cone on a nearly K\"ahler manifold…

We investigate Yang-Mills instantons on a 7-dimensional manifold of G_2 holonomy. By proposing a spherically symmetric ansatz for the Yang-Mills connection, we have ordinary differential equations as the reduced instanton equation, and give…

We study how a gluing construction, which produces compact manifolds with holonomy G_2 from matching pairs of asymptotically cylindrical G_2-manifolds, behaves under deformations. We show that the gluing construction defines a smooth map…

We deform classical holomorphic Chern--Simons theory on a Calabi--Yau three-fold $X$ by deforming the complex structure by a deformation parameter $h \in\mathscr{H}^{0,1}(T^{1,0}X)$. The corresponding equations of motion admit new…

We deal with instanton bundles on the product ${\mathbb P}^1\times{\mathbb P}^2$ and the blow up of ${\mathbb P}^3$ along a line. We give an explicit construction leading to instanton bundles. Moreover, we also show that they correspond to…

We construct novel classes of compact G2 spaces from lifting type IIA flux backgrounds with O6 planes. There exists an extension of IIA Calabi-Yau orientifolds for which some of the D6 branes (required to solve the RR tadpole) are dissolved…

A natural approach to the construction of nearly G2 manifolds lies in resolving nearly G2 spaces with isolated conical singularities by gluing in asymptotically conical G2 manifolds modelled on the same cone. If such a resolution exits, one…

Structure group SU(4) gauge vacua of both weakly and strongly coupled heterotic superstring theory compactified on torus-fibered Calabi-Yau threefolds Z with Z_2 x Z_2 fundamental group are presented. This is accomplished by constructing…

We study the physics of globally consistent four-dimensional $\mathcal{N}=1$ supersymmetric M-theory compactifications on $G_2$ manifolds constructed via twisted connected sum; there are now perhaps fifty million examples of these…

We investigate instantons on manifolds with Killing spinors and their cones. Examples of manifolds with Killing spinors include nearly Kaehler 6-manifolds, nearly parallel G_2-manifolds in dimension 7, Sasaki-Einstein manifolds, and…

We present some results on instanton corrections to the hypermultiplet moduli space in Calabi-Yau compactifications of Type II string theories. Previously, using twistor methods, only a class of D-instantons (D2-instantons wrapping…

We construct a compact, simply connected manifold with holonomy $\mathrm{G}_2$ that is non-formal. We use the construction method of compact torsion-free $\mathrm{G}_2$ manifolds developed by D.D. Joyce and S. Karigiannis. A non-vanishing…

We give a complete description of the behaviour of Calabi-Yau instantons and monopoles with an $SU(2)^2$-symmetry, on Calabi-Yau 3-folds with asymptotically conical geometry and $SU(2)^2$ acting with co-homogeneity one. We consider gauge…

Type IIA string theory compactified on a Calabi-Yau threefold has a hypermultiplet moduli space whose metric is known to receive non-perturbative corrections from Euclidean D2-branes wrapped on 3-cycles. These corrections have been computed…

We follow the idea of gluing theory in instanton moduli spaces and discuss the case when there is a finite group $\Gamma$ acting on the 4-manifolds $X_1, X_2$ with $x_1, x_2$ as isolated fixed points, how to glue two $\Gamma$-invariant ASD…