nLab vortex string

Idea

By a vortex string one typically means a string-shaped soliton threading through a vortex-solution in a 4-dimensional gauge theory.

The original example are the magnetic flux tubes through the Abrikosov vortices seen in type II superconductors at critical values of the magnetic field. The idea to think of these as string-like dynamical objects in themselves, much as in string theory, is due to Nielsen-Olesen 73, hence one also speaks of Nielsen-Oleson vortices or Nielsen-Olesen strings.

More generally, such string-shaped vortices are considered in Yang-Mills theories with non-abelian gauge group (see e.g. Tong 09).

Related cocepts

• Abrikosov vortex

• cosmic string

• defect brane

References

In electromagnetism

Vortex strings were originally considered in the abelian gauge theory of electromagnetism as Abrikosov vortices in type II superconductors.

• Alexei Abrikosov, On the Magnetic properties of superconductors of the second group, Sov. Phys. JETP 5 (1957) 1174-1182, Zh. Eksp. Teor. Fiz. 32 (1957) 1442-1452 (spire:9138)

The idea that these vortex flux tube could be thought of as dynamical strings much as in string theory is due to:

• Holger Bech Nielsen, Poul Olesen, Vortex-line models for dual strings, Nuclear Physics B Volume 61, 24 September 1973, Pages 45-61 (doi:10.1016/0550-3213(73)90350-7)

See also

• Wikipedia, Nielsen-Olesen vortex

In Yang-Mills theory

A more general picture of vortex strings in Yang-Mills theory with nonabelian gauge group (in fact in D=4 N=2 super Yang-Mills theory):

• Amihay Hanany, David Tong, Vortices, Instantons and Branes, JHEP 0307 (2003) 037 (arXiv:hep-th/0306150)

• Amihay Hanany, David Tong, Vortex Strings and Four-Dimensional Gauge Dynamics, JHEP 0404 (2004) 066 (arXiv:hep-th/0403158)

reviewed in:

• David Tong, Quantum Vortex Strings: A Review, Annals Phys. 324:30-52, 2009 (arXiv:0809.5060)

• David Tong, Vortices, Strings, and Vortex Strings (pdf)

As probe D1-branes of D1-D5 brane bound states in a context of AdS-QCD duality:

• Joseph Polchinski, Matthew Strassler, p. 34 of: The String Dual of a Confining Four-Dimensional Gauge Theory (arXiv:hep-th/0003136)

• Roberto Auzzi, S. Prem Kumar, Section 5.2 in: Non-Abelian k-Vortex Dynamics in $\mathcal{N} = 1^\ast$ theory and its Gravity Dual, JHEP 0812:077, 2008 (arXiv:0810.3201)

On vortex strings in $\mathcal{N}=2$ super QCD identified as superstrings in type II string theory compactified on a conifold:

• Mikhail Shifman, A. Yung, Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories, Rev. Mod. Phys. 79 1139 (2007) [doi:10.1103/RevModPhys.79.1139, arXiv:hep-th/0703267

• Mikhail Shifman, A. Yung, Supersymmetric Solitons, Cambridge University Press (2009) [doi:10.1017/CBO9780511575693]

• Mikhail Shifman, A. Yung, Critical String from Non-Abelian Vortex in Four Dimensions,

  Physics Letters B 750 (2015) 416-419 [arXiv:1502.00683, doi:10.1016/j.physletb.2015.09.045 ]

• P. Koroteev, Mikhail Shifman, A. Yung, Studying Critical String Emerging from Non-Abelian Vortex in Four Dimensions, Phys.Lett. B 759 (2016) 154-158 [arXiv:1605.01472, doi:10.1016/j.physletb.2016.05.075 ]