Related papers: Nahm transform for doubly-periodic instantons
This work concerns the study of certain finite-energy solutions of the anti-self-dual Yang-Mills equations on Euclidean 4-dimensional space which are periodic in two directions, so-called doubly-periodic instantons. We establish a circle of…
We explore the role played by the spectral curves associated with Higgs pairs in the context of the Nahm transform of doubly-periodic instantons defined in "Construction of doubly-periodic instantons" (math.DG/9909069) and "Nahm transform…
We construct finite energy instanton connection on $R^4$ which are periodic in two directions via an analogue of the Nahm transform for certain singular solutions of Hitchin's equations defined over a 2-torus.
We construct the Nahm transform from finite energy instantons on the product of a real line and a three dimensional torus to Dirac-type singular monopoles on the dual torus. Moreover, we show the correspondence between the data which handle…
This paper establishes that the Nahm transform sending spatially periodic instantons (instantons on the product of the real line and a three-torus) to singular monopoles on the dual three-torus is indeed a bijection as suggested by the…
Instantons on various spaces can be constructed via a generalization of the Fourier transform called the ADHM-Nahm transform. An explicit use of this construction, however, involves rather tedious calculations. Here we derive a simple…
Using the Nahm transform we investigate doubly periodic charge one SU(2) instantons with radial symmetry. Two special points where the Nahm zero modes have softer singularities are identified as the locations of instanton core constituents.…
We find the general hyper-elliptic solutions to the two-component reduced Nahm equations proposed by Hitchin et al. Elliptic solutions are a special case and can appear only for specific values of the monopole charges.
Calorons (periodic instantons) are anti-self-dual (ASD) connections on S^1 \times R^3 and form an intermediate case between instantons and monopoles. The ADHM and Nahm constructions of instantons and monopoles can be regarded as…
We study doubly-periodic instantons, i.e. instantons on the product of a 1-dimensional complex torus T with a complex line C, with quadratic curvature decay. We determine the asymptotic behaviour of these instantons, constructing new…
The main result is a computation of the Nahm transform of a SU(2)-instanton over RxT^3, called spatially-periodic instanton. It is a singular monopole over T^3, a solution to the Bogomolny equation, whose rank is computed and behavior at…
Using the Nahm transform we investigate doubly periodic charge one SU(2) instantons with radial symmetry. Two special points where the Nahm zero modes have softer singularities are identified as constituent locations. To support this…
Self-dual Yang-Mills instantons on $R^4$ correspond to algebraic ADHM data. The ADHM equations for $S^1$-symmetric instantons give a one-dimensional integrable lattice system, which may be viewed as an discretization of the Nahm equations.…
We embed the multi-fractional instantons of $SU(N)$ gauge theories on $\mathbb T^4$ with 't Hooft twisted boundary conditions into $U(N)$ bundles and use the Nahm transform to study the corresponding configurations on the dual…
We review the construction known as the Nahm transform in a generalized context, which includes all the examples of this construction already described in the literature. The Nahm transform for translation invariant instantons on $\real^4$…
We construct the Nahm transform for Higgs bundles over a Riemann surface of genus at least 2 as hyperholomorphic connections on the total space of the tangent bundle of its dual Jacobian.
In this paper, we complete the proof of an equivalence given by Nye and Singer of the equivalence between calorons (instantons on $S^1\times R^3$) and solutions to Nahm's equations over the circle, both satisfying appropriate boundary…
A typical solution of an integrable system is described in terms of a holomorphic curve and a line bundle over it. The curve provides the action variables while the time evolution is a linear flow on the curve's Jacobian. Even though the…
We discuss the Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction of U(N) instantons in noncommutative (NC) space and prove the one-to-one correspondence between moduli spaces of the noncommutative instantons and the ADHM data, together with…
We reconsider the large $N$ asymptotics of Harish-Chandra-Itzykson-Zuber integrals. We provide, using Dyson's Brownian motion and the method of instantons, an alternative, transparent derivation of the Matytsin formalism for the unitary…