Related papers: Dimension Reduction of Generalized ASD Instantons

We Study instanton solutions in general relativity with a scalar field. The metric ansatz we use is composed of a particular warp product of general Einstein metrics, such as those found in a number of cosmological settings, including…

Casson-type invariants emerging from Donaldson theory over certain negative definite 4-manifolds were recently suggested by Andrei Teleman. These are defined by a count of a zero-dimensional moduli space of flat instantons. Motivated by the…

The moduli space of k G-instantons on R^4 for a classical gauge group G is known to be given by the Higgs branch of a supersymmetric gauge theory that lives on Dp branes probing D(p + 4) branes in Type II theories. For p = 3, these (3 + 1)…

The self-duality equations on a Riemann surface arise as dimensional reduction of self-dual Yang-Mills equations. Hitchin had showed that the moduli space ${\mathcal M}$ of solutions of the self-duality equations on a compact Riemann…

The information metric arises in statistics as a natural inner product on a space of probability distributions. In general this inner product is positive semi-definite but is potentially degenerate. By associating to an instanton its energy…

We study reducing invariants of modules related to certain homological properties. For modules of finite reducing projective dimension, we establish grade inequalities. We prove that if $\mathbb{P}$ is the (uniform) Auslander condition, or…

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…

For a semisimple real Lie group $G$, we study topological properties of moduli spaces of polystable parabolic $G$-Higgs bundles over a Riemann surface with a divisor of finitely many distinct points. For a split real form of a complex…

We study one-instantons, that is anti-selfdual connections with instanton number 1, on the quantum projective plane with orientation which is reversed with respect to the usual one. The orientation is fixed by a suitable choice of a basis…

Let ${\mathcal I}(n)$ denote the moduli space of rank $2$ instanton bundles of charge $n$ on ${\mathbb P}^3$. We know from several authors that ${\mathcal I}(n)$ is an irreducible, nonsingular and affine variety of dimension $8n-3$. Since…

Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds is an outstanding open problem. We address this issue by relating the quaternionic-Kahler metric on…

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…

By replacing the ordinary product with the so called $\star$-product, one can construct an analogue of the anti-self-dual Yang-Mills (ASDYM) equations on the noncommutative $\bbR^4$. Many properties of the ordinary ASDYM equations turn out…

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…

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…

The arcane ADHM construction of Yang-Mills instantons can be very naturally understood in the framework of D-brane dynamics in string theory. In this point-of-view, the mysterious auxiliary symmetry of the ADHM construction arises as a…

We completely determine, up to homeomorphism, which simply connected compact oriented 4-manifolds admit scalar-flat, anti-self-dual Riemannian metrics. The key new ingredient is a proof that the connected sum of five reverse-oriented…

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…

Let $E$ be a smooth bundle with fiber an $n$-dimensional real projective space $\mathbb{R}P^n$. We show that, if every fiber carries a positively curved pointwise strongly $1/4$-pinched Riemannian metric that varies continuously with…

By reduction along the time direction, black holes in 4 dimensions yield instantons in 3 dimensions. Each of these instantons contributes individually at order $\exp(-|Q|/g_s)$ to certain protected couplings in the three-dimensional…