nLab
Nahm's equation

Contents

Context

Chern-Weil theory

Algebraic Quantum Field Theory

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

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Contents

Idea

(…)

Properties

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)

References

General

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)

Review:

  • 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.