相关论文: On Sp(n)-Instantons and the Fourier-Mukai Transfor…

We study U(r) instantons on elliptic surfaces with a section and show that they are in one-one correspondence with spectral data consisting of a curve in the dual elliptic surface and a line bundle on that curve. We use relative…

We investigate instantons on sine-cones over Sasaki-Einstein and 3-Sasakian manifolds. It is shown that these conical Einstein manifolds are K"ahler with torsion (KT) manifolds admitting Hermitian connections with totally antisymmetric…

We construct examples of deformed Hermitian Yang-Mills connections and deformed Spin(7)-instantons (also called Spin(7) deformed Donaldson-Thomas connections) on the cotangent bundle of $\mathbb{C}\mathbb{P}^2$ endowed with the Calabi…

In this article we study the moduli space of conically singular instantons (or Hermitian Yang--Mills connections) with prescribed tangent connections over a 6-manifold equipped with an $\mathrm{SU}(3)$-structure. That is, we develop a…

Given two compact hyperk\"ahler surfaces $X$ and $Y$ and a holomorphic vector bundle $Q$ on $X\times Y$, which is a generalized instanton, one can define a Fourier-Mukai transform, which, under suitable assumptions, maps vector bundles on…

We consider a dimensional reduction of the (deformed) Hermitian Yang-Mills condition on $S^1$-invariant K\"ahler Einstein $6$-manifolds. This allows us to reformulate the (deformed) Hermitian Yang-Mills equations in terms of data on the…

We construct and classify $SU(3)$-invariant primitive Hermitian Yang-Mills connections and $Sp(2)$-instantons with gauge groups $S = S^1$ and $S = SO(3)$ over the Calabi manifold $X = T^*CP^2$, the unique non-flat, complete,…

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 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 develop the deformation theory of instantons on asymptotically conical $Spin(7)$-manifolds where the instanton is asymptotic to a fixed nearly $G_2$-instanton at infinity. By relating the deformation complex with spinors, we identify the…

We present a novel approach to the study of Yang-Mills instantons on quaternionic K\"ahler manifolds, based on an extension of the harmonic space method of constructing instantons on hyperk\"ahler manifolds. Our results establish a…

We examine ADHM multi-instantons in the conformal N=2 supersymmetric Sp(N) gauge theory with one anti-symmetric tensor and four fundamental hypermultiplets. We argue that the ADHM construction and measure can also be deduced from purely…

An instanton $(E, D)$ on a (pseudo-)hyperk\"ahler manifold $M$ is a vector bundle $E$ associated to a principal $G$-bundle with a connection $D$ whose curvature is pointwise invariant under the quaternionic structures of $T_x M, \ x\in M$,…

We study quiver gauge theories on the round and squashed seven-spheres, and orbifolds thereof. They arise by imposing $G$-equivariance on the homogeneous space $G/H=\mathrm{SU}(4)/\mathrm{SU}(3)$ endowed with its Sasaki-Einstein structure,…

We revisit the problem of constructing instantons on ADE orbifolds R^4/\Gamma and point out some subtle relations with the complex structure on the orbifold. We consider generalized instanton equations on R^4/\Gamma which are BPS equations…

We develop the gluing theory of contact instantons in the context of open strings and in the context of closed strings \emph{with vanishing charge}, for example in the symplectization context. This is one of the key ingredients for the…

We formulate the deformation theory for instantons on nearly K\"ahler six-manifolds using spinors and Dirac operators. Using this framework we identify the space of deformations of an irreducible instanton with semisimple structure group…

We interpret a class of 4k-dimensional instanton solutions found by Ward, Corrigan, Goddard and Kent as four-dimensional instantons at angles. The superposition of each pair of four-dimensional instantons is associated with four angles…

We consider the Hermitian Yang-Mills (instanton) equations for connections on vector bundles over a 2n-dimensional K\"ahler manifold X which is a product Y x Z of p- and q-dimensional Riemannian manifold Y and Z with p+q=2n. We show that in…

We study the deformation theory of $\mathrm{G}_2$-instantons on nearly $\mathrm{G}_2$ manifolds. There is a one-to-one correspondence between nearly parallel $\mathrm{G}_2$ structures and real Killing spinors, thus the deformation theory…