Related papers: $G_2$-instantons, associative submanifolds, and Fu…
We show that $QCD_2$ with adjoint fermions involves instantons due to nontrivial $\pi_1[SU(N)/Z_N]~=~Z_N$. At high temperatures, quasiclassical approximation works and the action and the form of effective (with account of quantum…
The purpose of this paper is to describe a relationship between the moduli space of vortices and the moduli space of instantons. We study charge k vortices in U(N) Yang-Mills-Higgs theories and show that the moduli space is isomorphic to a…
We prove an existence theorem for Spin(7)-instantons, which are highly concentrated near a Cayley submanifold; thus giving a partial converse to Tian's foundational compactness theorem. As an application, we show how to construct…
We study generalized anti-self-dual instantons defined over Riemannian manifolds equipped with a parallel codimension-$4$ differential form. In particular, for product Riemannian manifolds possessing such a form, we study dimension…
This paper is a short version of some joint work with Stefan Haller. It describes the structure of "smooth manifold with corners" on the space of possibly broken instantons and on the completion of unstable manifolds of a generic smooth…
Gieseker-Nakajima moduli spaces $M_{k}(n)$ parametrize the charge $k$ noncommutative $U(n)$ instantons on ${\bf R}^{4}$ and framed rank $n$ torsion free sheaves $\mathcal{E}$ on ${\bf C\bf P}^{2}$ with ${\rm ch}_{2}({\mathcal{E}}) = k$.…
In this paper we study ${\rm Spin}(7)$-instantons on asymptotically conical ${\rm Spin}(7)$-orbifolds (and manifolds) obtained by filling in certain squashed $3$-Sasakian $7$-manifolds. We construct a $1$-parameter family of explicit ${\rm…
We present a classification of SU(2) instantons on $T^2\times\mathbb{R}^2$ according to their asymptotic behaviour. We then study the existence of such instantons for different values of the asymptotic parameters, describing explicitly the…
On P3, we show that mathematical instantons in characteristic two are unobstructed. We produce upper bounds for the dimension of the moduli space of stable rank two bundles on P3 in characteristic two. In cases where there is a phenomenon…
Local aspects of singular F-theory compactifications for SUSY GUT model-building are fairly well understood in terms of Higgs bundles and their spectral data. Several global issues remain, however, including a description of G-fluxes, which…
The known calculations of the fermion condensate $<\bar{\psi}\psi>$ and the correlator $<\bar{\psi}\psi(x) ~\bar{\psi}\psi(0)>$ have been interpreted in terms of {\em localized} instanton solutions minimizing the {\em effective} action.…
We consider type IIA compactification on $K3$. We show that the instanton subsectors of the worldvolume of $N$ 4-branes wrapped around $K3$ lead to a Hagedorn density of BPS states in accord with heterotic-type IIA duality in 6 dimensions.…
This thesis is an investigation of the moduli spaces of instanton bundles on the Fano threefold $Y_5$ (a linear section of $\mathbb{G}r(2,5)$). It contains new proofs of classical facts about lines, conics and cubics on $Y_5$, and about…
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…
The moduli space of instantons on an ALE space is studied using the moduli space of $\mathcal{N}=4$ field theories in three dimensions. For instantons in a simple gauge group $G$ on $\mathbb{C}^2/\mathbb{Z}_n$, the Hilbert series of such an…
Instantons, emerged in particle physics, have been intensely studied since the 1970's and had an enormous impact in mathematics since then. In this paper, we focus on one particular way in which mathematical physics has guided the…
By fibering the duality between the $E_{8}\times E_{8}$ heterotic string on $T^{3}$ and M-theory on K3, we study heterotic duals of M-theory compactified on $G_{2}$ orbifolds of the form $T^{7}/\mathbb{Z}_{2}^{3}$. While the heterotic…
We give a construction of $G_2$ and $Spin(7)$ instantons on exceptional holonomy manifolds constructed by Bryant and Salamon, by using an ansatz of spherical symmetry coming from the manifolds being the total spaces of rank-4 vector…
We show the non-compactness of moduli space of solutions of the monopole equations for $3/2$-spinors on a closed 3-manifold is equivalent to the existence of `3/2-Fueter sections' that are solutions of an overdetermined non-linear elliptic…
Here we study the deformations of associative submanifolds inside a G_2 manifold M^7 with a calibration 3-form \phi. A choice of 2-plane field \Lambda on M (which always exits) splits the tangent bundle of M as a direct sum of a…