nLab ADHM construction

Contents

Idea

A method for constructing Yang-Mills instanton solutions. (ADHM)

Related concepts

• Nahm transform

• Skyrmion

References

The original articles:

• Michael Atiyah, Nigel Hitchin, Vladimir Drinfeld, Yuri Manin, Construction of instantons, Physics Letters A 65 3 (1978) 185-187 []

• Norman H. Christ, Erick J. Weinberg, and Nancy K. Stanton, General self-dual Yang-Mills solutions, Phys. Rev. D 18 6 (1978) [[doi:10.1103/PhysRevD.18.2013](https://doi.org/10.1103/PhysRevD.18.2013)]

  (emphasis on well-separated instanton solutions)

Surveys:

• Bert Lindenhovius, Instantons and the ADHM construction, Amsterdam (2011) [pdf]

• Nick Dorey, Timothy J. Hollowood, Valentin V. Khoze, Michael P. Mattis, The Calculus of Many Instantons, Phys. Rept. 371 (2002) 231-459 [[arXiv:hep-th/0206063](https://arxiv.org/abs/hep-th/0206063), doi:10.1016/S0370-1573(02)00301-0]

In 8 dimensions:

• Atsushi Nakamula, Shin Sasaki, Koki Takesue, ADHM construction of (anti-)self-dual instantons in eight dimensions, Nuclear Physics B 910 (2016) 199-224 [[arXiv:1604.01893](https://arxiv.org/abs/1604.01893), doi:10.1016/j.nuclphysb.2016.06.026]

For the relation to Skyrmions see there.