# Spectral curves and the ADHM method

@article{Hitchin1988SpectralCA, title={Spectral curves and the ADHM method}, author={N. Hitchin and M. 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.

#### 16 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… Expand

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… Expand

Spectral curves of non-integral hyperbolic monopoles

- Physics
- 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… Expand

On the Complete Integrability of the Discrete Nahm Equations

- Mathematics, Physics
- 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… Expand

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… Expand

Kac-Moody monopoles and periodic instantons

- Mathematics
- 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… Expand

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… Expand

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

- Physics
- 1989

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 = 1… Expand

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… Expand

Dirac zero modes for Abelian BPS multimonopoles

- Physics, Mathematics
- 2015

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 $\mathbb R^3$.

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- Mathematics
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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… Expand

Monopoles and geodesics

- Mathematics
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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… Expand

On the construction of monopoles

- Mathematics
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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 whose… Expand

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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… Expand

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