# Spectral curves and the ADHM method

@article{Hitchin1988SpectralCA, title={Spectral curves and the ADHM method}, author={Nigel James Hitchin and Michael K. Murray}, journal={Communications in Mathematical Physics}, year={1988}, volume={114}, pages={463-474} }

For a general monopole the algebraic curves defined by Nahm are shown to be the same as the spectral curves.

## 18 Citations

### Monopoles and their spectral data

- Mathematics
- 1990

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 maximal…

### A new approach to monopole moduli spaces

- Mathematics
- 2007

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. Using…

### Spectral curves of non-integral hyperbolic monopoles

- Mathematics
- 1996

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 hyperbolic…

### On the Complete Integrability of the Discrete Nahm Equations

- Mathematics
- 2000

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 Nahm…

### On the construction of monopoles for the classical groups

- Mathematics
- 1989

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 on…

### Kac-Moody monopoles and periodic instantons

- Physics
- 1988

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 spectral…

### Differential geometry of monopole moduli spaces

- Mathematics
- 2006

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 hyperbolic…

### Topological invariants and a gauge theory of the super-Poincaré algebra in three dimensions

- Mathematics, Physics
- 1989

### Symmetric Monopoles

- Mathematics
- 1994

We discuss the spectral curves and rational maps associated with SU (2) Bogomolny monopoles of arbitrary charge k . We describe the eﬀect on the rational maps of inverting monopoles in the plane with…

### Stratifying monopoles and rational maps

- Mathematics
- 1989

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 these…

## References

SHOWING 1-7 OF 7 REFERENCES

### Monopoles and spectral curves for arbitrary Lie groups

- Mathematics
- 1983

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 of…

### Monopoles and geodesics

- Mathematics
- 1982

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 by…

### Algebraic Geometry

- MathematicsNature
- 1973

Introduction to Algebraic Geometry.By Serge Lang. Pp. xi + 260. (Addison–Wesley: Reading, Massachusetts, 1972.)

### Non-Abelian magnetic monopoles

- Mathematics
- 1984

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 is…

### On the Construction of Monopoles for

- Physics
- 1989

Monopoles are solutions of a first order partial differential equation — the Bogomolny equation. They can be thought of as approximated by static, magnetic particles in R. In these notes we will…

### Linear field equations on self-dual spaces

- MathematicsProceedings 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 a…

### The algebraic geometry of multimonopoles

- Physics
- 1983

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 local…