Nahm's equation



Chern-Weil theory

Algebraic Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)



field theory:

Lagrangian field theory


quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization



States and observables

Operator algebra

Local QFT

Perturbative QFT





In string theory

Transversal Dp-D(p+2)-brane intersections geometrically engineer Yang-Mills monopoles: their moduli space is the moduli space of monopoles/solutions of Nahm's equation

(Diaconescu 97, Hanany-Zaffaroni 99)



The original articles;

  • Werner Nahm, The construction of all self-dual multi-monopoles by the ADHM method, In: Craigie et al. (eds.), Monopoles in quantum theory, Singapore, World Scientific 1982 (spire:178340)

  • Werner Nahm, Self-dual monopoles and calorons, In: G. Denardo, G. Ghirardi and T. Weber (eds.), Group theoretical methods in physics, Lecture Notes in Physics 201. Berlin, Springer-Verlag 1984 (doi:10.1007/BFb0016145)

  • Simon Donaldson, Nahm’s Equations and the Classification of Monopoles, Comm. Math. Phys., Volume 96, Number 3 (1984), 387-407, (euclid:cmp.1103941858)

Further discussion:

  • Rafe Mazzeo, Edward Witten, The Nahm Pole Boundary Condition, In: The influence of Solomon Lefschetz in geometry and topology, Contemporary Mathematics 621 (2014): 171 (doi:10.1090/conm/621)


  • Marcos Jardim, A survey on Nahm transform, J Geom Phys 52 (2004) 313-327 (arxiv:math/0309305)

  • Reinier Storm, The Yang-Mills Moduli Space and The Nahm Transform (dspace:1874/285043)

See also

In terms of Coulomb branch singularities in SYM

In terms of Coulomb branch singularities on super Yang-Mills theories:

In term of Dp-D(p+2) brane intersections

On transversal Dp-D(p+2) brane intersections as Yang-Mills monopoles / fuzzy funnel-solutions to Nahm's equation:

For transversal D1-D3 brane intersections:

For transversal D2-D4-brane bound states (with an eye towards AdS/QCD):

  • Alexander Gorsky, Valentin Zakharov, Ariel Zhitnitsky, On Classification of QCD defects via holography, Phys. Rev. D79:106003, 2009 (arxiv:0902.1842)

For transversal D3-D5 brane intersections:

For transversal D6-D8 brane intersections (with an eye towards AdS/QCD):

  • Deog Ki Hong, Ki-Myeong Lee, Cheonsoo Park, Ho-Ung Yee, Section V of: Holographic Monopole Catalysis of Baryon Decay, JHEP 0808:018, 2008 (https:arXiv:0804.1326)

and as transversal D6-D8-brane bound states on a half NS5-brane in type I' string theory:

Lift to M-theory

The lift of Dp-D(p+2)-brane bound states in string theory to M2-M5-brane bound states/E-strings in M-theory, under duality between M-theory and type IIA string theory+T-duality, via generalization of Nahm's equation (this eventually motivated the BLG-model/ABJM model):

Last revised on December 5, 2019 at 08:55:57. See the history of this page for a list of all contributions to it.