Related papers: Yang-Mills fields in flux compactifications on hom…

Interpreting the coordinates of the quantum Euclidean space R_q^4 [the SO_q(4)-covariant noncommutative space] as the entries of a ``q-quaternion matrix'' we construct (anti)instanton solutions of a would-be q-deformed su(2) Yang-Mills…

We find exact multi-instanton solutions to the selfdual Yang-Mills equation on a large class of curved spaces with $SO(3)$ isometry, generalizing the results previously found on $\mathbb{R}^4$. The solutions are featured with explicit…

Anti-self-dual (ASD) solutions to the Yang-Mills equation (or instantons) over an anti-self-dual four manifold, which are invariant under an appropriate action of a three dimensional Lie group, give rise, via twistor construction, to…

This is a self-contained set of lecture notes on instantons in (super) Yang-Mills theory in four dimensions and in quantum mechanics. First the basics are derived from scratch: the regular and singular one-instanton solutions for Yang-Mills…

Motivated by the swampland program, we show that the Weil-Petersson geometry of the moduli space of a Calabi-Yau manifold of complex dimension $d\leq4$ is a gravitational instanton (i.e. a finite-action solution of the Euclidean equations…

We present a general procedure to construct 6-dimensional manifolds with SU(3)-structure from SU(2)-structure 5-manifolds. We thereby obtain half-flat cylinders and sine-cones over 5-manifolds with Sasaki-Einstein SU(2)-structure. They are…

We investigate Yang-Mills instantons on a 7-dimensional manifold of G_2 holonomy. By proposing a spherically symmetric ansatz for the Yang-Mills connection, we have ordinary differential equations as the reduced instanton equation, and give…

We construct the n-instanton action for the above model with gauge group SU(2), as a function of the collective coordinates of the general self-dual configurations of Atiyah, Drinfeld, Hitchin and Manin (ADHM). We calculate the quantum…

We present and discuss BPS instanton solutions that appear in type II string theory compactifications on Calabi-Yau threefolds. From an effective action point of view these arise as finite action solutions of the Euclidean equations of…

We consider self-dual Yang-Mills instantons in 4-dimensional Kaehler spaces with one holomorphic isometry and show that they satisfy a generalization of the Bogomol'nyi equation for magnetic monopoles on certain 3-dimensional metrics. We…

Structure group SU(4) gauge vacua of both weakly and strongly coupled heterotic superstring theory compactified on torus-fibered Calabi-Yau threefolds Z with Z_2 x Z_2 fundamental group are presented. This is accomplished by constructing…

We present a unified eight-dimensional approach to instanton equations on several seven-dimensional manifolds associated to a six-dimensional homogeneous nearly K\"ahler manifold. The cone over the sine-cone on a nearly K\"ahler manifold…

We construct analytical self-dual Yang-Mills fractional instanton solutions on a four-torus $\mathbb{T}^4$ with 't Hooft twisted boundary conditions. These instantons possess topological charge $Q=\frac{r}{N}$, where $1\leq r< N$. To…

We consider pure $SU(2)$ Yang-Mills theory when the space is compactified to a 3-dimensional sphere with finite radius. The Euclidean classical self-dual solutions of the equations of motion (the instantons) and the static finite energy…

Subjecting the SU(2) Yang--Mills system to azimuthal symmetries in both the $x-y$ and the $z-t$ planes results in a residual subsystem described by a U(1) Higgs like model with two complex scalar fields on the quarter plane. The resulting…

We derive the explicit formula for fractional BPS lumps (or fractional instantons) in the $\mathbb{C}P^{N-1}$ nonlinear sigma model on a two-dimensional torus under various shift-clock twisted boundary conditions. After regularizing the…

We present a semiclassical calculation of instanton effects in N=4 supersymmetric Yang-Mills theory formulated on R^{3}XS^{1} and also in the N=1 theory obtained by introducing chiral multiplet masses. In the N=4 case, these instanton…

In this paper we show how hypercomplex function theoretical objects can be used to construct explicitly self-dual SU(2)-Yang-Mills instanton solutions on certain classes of conformally flat 4-manifolds. We use a hypercomplex argument…

We study N=4 supersymmetric Yang-Mills (SYM) theory with gauge group SU(2) compactified to three dimensions on a circle of circumference beta. The eight fermion terms in the effective action on the Coulomb branch are determined exactly, for…

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…