Spectral curves and the ADHM method

  title={Spectral curves and the ADHM method},
  author={N. Hitchin and M. Murray},
  journal={Communications in Mathematical Physics},
For a general monopole the algebraic curves defined by Nahm are shown to be the same as the spectral curves. 
Monopoles and their spectral data
A new definition of spectral data of a monopole is given for any compact Lie or Kac-Moody group. It is shown that the spectral data determines the irreducible monopole. In the case of maximalExpand
A new approach to monopole moduli spaces
We introduce a new way to study both Euclidean and hyperbolic monopole moduli spaces. The idea is to apply Kodaira's deformation theory to the spectral curve in an appropriate ambient space. UsingExpand
Spectral curves of non-integral hyperbolic monopoles
The twistor desription of non-integral -monopoles on hyperbolic 3-space is developed and some consequences discussed. It is shown that in a precise sense, any appropriately decaying hyperbolicExpand
On the Complete Integrability of the Discrete Nahm Equations
Abstract: The discrete Nahm equations, a system of matrix valued difference equations, arose in the work of Braam and Austin on half-integral mass hyperbolic monopoles.We show that the discrete NahmExpand
On the construction of monopoles for the classical groups
ForG a classical group, an equivalence is exhibited between:A)G monopoles over ℝ3, with maximal symmetry breaking at infinity,B)families of (rank (G)) algebraic curves inTℙ1, along with divisors onExpand
Kac-Moody monopoles and periodic instantons
It is shown that calorons, or periodic instantons are the same as monopoles with the loop group as their structure group. Their twistor correspondences and spectral data are defined. The spectralExpand
Differential geometry of monopole moduli spaces
This thesis was motivated by a desire to understand the natural geometry of hyperbolic monopole moduli spaces. We take two approaches. Firstly we develop the twistor theory of singular hyperbolicExpand
Topological invariants and a gauge theory of the super-Poincaré algebra in three dimensions
Abstract Various aspects of superspace topology and N = 1 supersymmetry in 2 + 1 dimensions are explored. Non-minimal super Yang-Mills theory is used to construct a gauge theory of the N = 1Expand
Stratifying monopoles and rational maps
A stratification of the moduli space of monopoles and of the space of rational maps into a flag variety is presented. It is shown that the map associating a rational map to a monopole preserves theseExpand
Dirac zero modes for Abelian BPS multimonopoles
We develop a method for finding the zero modes of the Dirac operator in the presence of BPS monopoles. We use it to find the zero modes in the case of Abelian BPS monopoles in $\mathbb R^3$.


Monopoles and spectral curves for arbitrary Lie groups
The definition of the spectral curve of a monopole is extended to any connected, compact, simple Lie groupK. It is found there are rankK curves whose degrees are related to the topological weights ofExpand
Monopoles and geodesics
AbstractUsing the holomorphic geometry of the space of straight lines in Euclidean 3-space, it is shown that every static monopole of chargek may be constructed canonically from an algebraic curve byExpand
On the construction of monopoles
We show that any self-dual SU (2) monopole may be constructed either by Ward's twistor method, or Nahm's use of the ADHM construction. The common factor in both approaches is an algebraic curve whoseExpand
Non-Abelian magnetic monopoles
It is shown that a general, irreducible, SU(n), Sp(n), SO(2n) monopole with maximal symmetry breaking is determined by its spectral data. For SU(n) with minimal symmetry breaking the spectral data isExpand
Linear field equations on self-dual spaces
  • N. Hitchin
  • Mathematics
  • Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1980
In a Riemannian context, a description is given of the Penrose correspondence between solutions of the anti-self-dual zero rest-mass field equations in a self-dual Yang-Mills background on aExpand
The algebraic geometry of multimonopoles
Let G be the symmetry group of the laws of nature. The physical vacuum is not invariant under G, but only under a subgroup H. Thus any element of the coset space G/H yields a different possible localExpand