Related papers: Current progress on $G_2$--instantons over twisted…
In this paper we show that conifold transitions between Calabi-Yau 3-folds can be used for the construction of mirror manifolds and for the computation of the instanton numbers of rational curves on complete intersection Calabi-Yau 3-folds…
Recently, Kallen and Zabzine computed the partition function of a twisted supersymmetric Yang-Mills theory on the five-dimensional sphere using localisation techniques. Key to their construction is a five-dimensional generalisation of the…
We consider geodesics of infinite length and constant 4d dilaton in the (classical) hypermultiplet moduli space of type II Calabi-Yau compactifications. When approaching such infinite distance points, a large amount of D-instantons develop…
The dimensional reduction of eleven dimensional supergravity on a Calabi-Yau manifold gives N=2 supergravity in five dimensions with $h_{1,1}$ vector and $h_{2,1}+1$ hypermultiplets. In this paper instanton solutions are constructed which…
Type IIA orientifold constructions with intersecting D6-branes and their IIB duals in terms of magnetized D9/D7-branes constitute one of the most promising avenues for the construction of semirealistic MSSM-like compactifications. One…
Given an integer b and a finitely presented group G we produce a compact symplectic six-manifold with c_1 = 0, b_2 > b, b_3 > b and fundamental group G. In the simply-connected case we can also arrange for b_3 = 0; in particular these…
We prove the derived equivalence of a pair of non-compact Calabi-Yau 7-folds, which are the total spaces of certain rank 2 bundles on $G_2$-Grassmannians. The proof follows that of the derived equivalence of Calabi-Yau 3-folds in…
The SL(2,C) Yang-Mills instanton solutions constructed recently by the biquaternion method were shown to satisfy the complex version of the ADHM equations and the Monad construction. Moreover, we discover that, in addition to the…
We discuss general properties of strong G$_2$-structures with torsion and we investigate the twisted G$_2$ equation, which represents the G$_2$-analogue of the twisted Calabi-Yau equation for SU$(n)$-structures introduced by…
We construct new type II ancient compact solutions to the Yamabe flow. Our solutions are rotationally symmetric and converge, as $t \to -\infty$, to a tower of two spheres. Their curvature operator changes sign. We allow two time-dependent…
We study the moduli spaces of self-dual instantons on CP^2 in a simple group G. When G is a classical group, these instanton solutions can be realised using ADHM-like constructions which can be naturally embedded into certain three…
We study a two parameter family of Calabi-Yau d-fold by means of mirror symmetry. We construct mirror maps and calculate correlation functions associated with {\kae} moduli in the original manifold. We find there are more complicated…
We analyse the non-perturbative superpotential due to M5-brane instantons in F-theory compactifications on Calabi-Yau fourfolds. The M5 partition function is obtained via holomorphic factorisation by explicitly performing the sum over…
This paper contains the results of our investigations of BPS instantons and of our work on N=2 supersymmetric gauge theories. The BPS instantons we study appear in type II string theory compactifications on Calabi-Yau threefolds. In the…
We investigate nonperturbative effects in M-theory compactifications arising from wrapped membranes. In particular, we show that in $d=4, \mathcal{N}=1$ compactifications along manifolds of $G_2$ holonomy, membranes wrapped on rigid…
We investigate membrane instanton effects in type IIA strings compactified on rigid Calabi-Yau manifolds. These effects contribute to the low-energy effective action of the universal hypermultiplet. In the absence of additional fivebrane…
We propose new $G_2$-holonomy manifolds, which geometrize the Gaiotto-Kim 4d N=1 duality domain walls of 5d N=1 theories. These domain walls interpolate between different extended Coulomb branch phases of a given 5d superconformal field…
We introduce the notion of an instanton bundle on a Fano threefold of index 2. For such bundles we give an analogue of a monadic description and discuss the curve of jumping lines. The cases of threefolds of degree 5 and 4 are considered in…
We consider $G_2$-structures with torsion coupled with $G_2$-instantons, on a compact $7$-dimensional manifold. The coupling is via an equation for $4$-forms which appears in supergravity and generalized geometry, known as the Bianchi…
In this paper we present a construction of stable bundles on Calabi-Yau threefolds using the method of bundle extensions. This construction applies to any given Calabi-Yau threefold with h^{1,1}>1. We give examples of stable bundles of rank…