Related papers: Isomonodromic deformations and SU2-invariant insta…

Several results on existence and convergence of the Yang-Mills flow in dimension four are given. We show that a singularity modeled on an instanton cannot form within finite time. Given low initial self-dual energy, we then study…

Multi-parametric families of AdS$_{4}$ vacua with various amounts of supersymmetry and residual gauge symmetry are found in the $\,[\textrm{SO}(1,1) \times \textrm{SO}(6)] \ltimes \mathbb{R}^{12}\,$ maximal supergravity that arises from the…

In this work we study the dimensional reduction of smooth circle invariant Yang-Mills instantons defined on 4-manifolds which are non-trivial circle fibrations over hyperbolic 3-space. A suitable choice of the 4-manifold metric within a…

In these lectures, which are written at an elementary and pedagogical level, we discuss general aspects of (single) instantons in SU(N_c) Yang-Mills theory, and then specialize to the case of N = 4 supersymmetry and the large N_c limit. We…

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,…

New static regular axially symmetric solutions of SU(2) Euclidean Yang-Mills theory are constructed numerically. They represent calorons having trivial Polyakov loop at spacial infinity. The solutions are labeled by two integers $m,n$. It…

We explore the deformation theory of instantons on locally conformal (LC) $Spin(7)$ manifolds. These structures, characterized by a non-parallel fundamental 4-form $\Phi$ satisfying $d\Phi = \theta \wedge \Phi$, represent a significant, yet…

We consider two simple examples of multi-instanton configurations in type II 4d N=1 superstring compactifications. The first one involves O(1) and U(1) D2-instantons embedded in T^6/(Z_2 x Z_2') geometry with SU(4) gauge symmetry coming…

The moduli space of self-dual $SU(N)$ Yang-Mills instantons on $\mathbb T^4$ of topological charge $Q = r/N$, $1 \leq r \leq N-1$, is of current interest, yet is not fully understood. In this paper, starting from 't Hooft's constant field…

We prove an energy identity for anti-self-dual connections on the product C\times\Sigma of the complex plane and a Riemann surface. The energy is a multiple of a basic constant that is determined from the values of a corresponding…

We calculate the instanton partition function of the four-dimensional N=2* SU(N) gauge theory in the presence of a generic surface operator, using equivariant localization. By analyzing the constraints that arise from S-duality, we show…

The Vafa-Witten equations on an oriented Riemannian 4- manifold are first order, non-linear equations for a pair of connection on a principle SO(3) bundle over the 4-manifold and a self-dual 2-form with values in the associated Lie algebra…

We analyse the most general N=2 supersymmetric solutions of D=11 supergravity consisting of a warped product of four-dimensional anti-de-Sitter space with a seven-dimensional Riemannian manifold Y_7. We show that the necessary and…

We propose a method to construct G_2-instantons over a compact twisted connected sum G_2-manifold, applying a gluing result of S\'a Earp and Walpuski to instantons over a pair of 7-manifolds with a tubular end (see arXiv:1310.7933). In our…

We compute the infinitesimal deformations of quadruples of the form $$(X, S, E_*, D),$$ where $(X, S)$ is a compact Riemann surface with $n$ marked points, $E_*$ is a parabolic vector bundle on $X$ with parabolic structure over $S$, and $D$…

The total space of the spinor bundle on the four dimensional sphere S^4 is a quaternionic line bundle that admits a metric of Spin(7) holonomy. We consider octonionic Yang-Mills instanton on this eight dimensional gravitational instanton.…

We consider the action on instanton moduli spaces of the non-local symmetries of the self-dual Yang-Mills equations on $\mathbb{R}^4$ discovered by Chau and coauthors. Beginning with the ADHM construction, we show that a sub-algebra of the…

SL(2,Z) duality transformations in asymptotically AdS4 x S^7 act non-trivially on the three-dimensional SCFT of coincident M2-branes on the boundary. We show how S-duality acts away from the IR fixed point. We develop a systematic method to…

We introduce a diffeomorphism invariant of $4$-manifolds, the $\mathrm{Pin}^-(2)$-monopole invariant, defined by using the $\mathrm{Pin}^-(2)$-monopole equations. We compute the invariants of several $4$-manifolds, and prove gluing…

We show that for every Sasaki-Einstein manifold, $M_5$, the AdS$_5\times M_5$ background of type IIB supergravity admits two universal deformations leading to supersymmetric AdS$_4$ solutions. One class of solutions describes an AdS$_4$…