Related papers: $\mathrm{G}_2$-instantons on the 7-sphere

Bryant and Salamon gave a construction of metrics of G2 holonomy on the total space of the bundle of anti-self-dual (ASD) 2-forms over a 4-dimensional self-dual Einstein manifold. We generalise it by considering the total space of an SO(3)…

We describe an approach to the noncommutative instantons on the 4-sphere based on quantum group theory. We quantize the Hopf bundle S^7 --> S^4 making use of the concept of quantum coisotropic subgroups. The analysis of the semiclassical…

In this article we consider a path integral formulation of the Hubbard model based on a SU(2)-symmetrical Hubbard-Stratonovich transformation that couples auxiliary field to the local electronic density. This decoupling is known to have a…

In this note I review the construction of higher-dimensional instantons and heterotic NS5-branes on Ricci-flat cones from arXiv:1109.3552, as well as fractional strings from arXiv:1202.5046. The focus is on methods and interpretation. I…

We consider Lie G-valued Yang-Mills fields on the space R x G/H, where G/H is a compact nearly K"ahler six-dimensional homogeneous space, and the manifold R x G/H carries a G_2-structure. After imposing a general G-invariance condition,…

This paper is dedicated to the study of deformations of coassociative 4-folds in a G_2 manifold which have conical singularities. We stratify the types of deformations allowed into three problems. The main result for each problem states…

We discuss instantons in dimensions higher than four. A generalized self-dual or anti-self-dual instanton equation in n-dimensions can be defined in terms of a closed (n-4) form $\Omega$ and it was recently employed as a topological gauge…

Gravitational instantons ''Lambda-instantons'' are defined here for any given value Lambda of the cosmological constant. A multiple of the Euler characteristic appears as an upper bound for the de Sitter action and as a lower bound for a…

We overview the properties of non-infinitesimal deformations of G2-structures on seven-manifolds, and in particular, focus on deformations that lie in the seven-dimensional representation of G2 and are thus defined by a vector. We then…

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…

We consider a compact twistor space P and assume that there is a surface S in P, which has degree one on twistor fibres and contains a twistor fibre F, e.g. P a LeBrun twistor space. Similar to Donaldson and Buchdahl we examine the…

We introduce and study tetrahedron instantons, which can be realized in string theory by D$1$-branes probing a configuration of intersecting D$7$-branes in flat spacetime with a proper constant $B$-field. Physically they capture instantons…

We construct $\theta$-deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative four-sphere $S^4_\theta$, we construct a noncommutative family of instantons of charge 1. The family is…

We introduce and study a surface defect in four dimensional gauge theories supporting nested instantons with respect to the parabolic reduction of the gauge group at the defect. This is engineered from a D3/D7-branes system on a non compact…

We obtain three and four dimensional conformal field theories with less than maximal supersymmetry by using their supergravity duals. These supergravity theories are type II on $AdS_5 \times CP^2$, IIA on $AdS_4 \times CP^3$, IIB on $AdS_5…

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…

The Leigh-Strassler family of N=1 marginal deformations of the N=4 SYM theory admits a Hopf algebra symmetry which is a quantum group deformation of the SU(3) part of the R-symmetry of the Ncal=4 theory. We investigate how this quantum…

In this paper, we study gravitational instantons (i.e., complete hyperk\"aler 4-manifolds with faster than quadratic curvature decay). We prove three main theorems: 1.Any gravitational instanton must have known end----ALE, ALF, ALG or ALH.…

We study instanton-corrected renormalization group flow in the two dimensional sigma models and four dimensional gauge theory. In two dimensions we do that by replacing the non-linear supersymmetric ${\IC\IP}^{N-1}$ model by the gauged…

We analyze the instanton transitions in the framework of the gauge invariant variational calculation in the pure Yang-Mills theory. Instantons are identified with the saddle points in the integration over the gauge group which projects the…