Hitchin's equations and integrability of BPS Z(N) strings in Yang-Mills theories

@article{Kneipp2008HitchinsEA,
  title={Hitchin's equations and integrability of BPS Z(N) strings in Yang-Mills theories},
  author={Marco A.C. Kneipp},
  journal={Journal of High Energy Physics},
  year={2008},
  volume={2008},
  pages={049-049}
}
  • M. Kneipp
  • Published 4 January 2008
  • Mathematics
  • Journal of High Energy Physics
We show that ZN string's BPS equations are equivalent to the Hitchin's equations (or self-duality equation) and also to the zero curvature condition. We construct the general form for BPS ZN string solutions for arbitrary simple gauge groups with non-trivial center. Depending on the vacuum solutions considered, the ZN string's BPS equations reduce to different two dimensional integrable field equations. For a particular vacuum we obtain the equation of affine Toda field theory. 
View PDF on arXiv
12 Citations
Background Citations
3

12 Citations

BPS Z N string tensions, sine law and Casimir scaling, and integrable field theories

We consider a Yang-Mills-Higgs theory with spontaneous symmetry breaking of the gauge group G → U(1) r → C G , with C G being the center of G. We study two vacua solutions of the theory which produce…

Infinitely many conservation laws in self-dual Yang-Mills theory

Using a nonlocal field transformation for the gauge field known as Cho-Faddeev-Niemi-Shabanov decomposition as well as ideas taken from generalized integrability, we derive a new family of infinitely…

Z(2) monopoles in SU(n) Yang-Mills-Higgs theories

Z{sub n} monopoles are important for the understanding of the Goddard-Nuyts-Olive duality when the scalar field is not in the adjoint representation. We analyze the Z{sub 2} monopole solutions in…

Symmetries of self-dual Yang-Mills equations dimensionally reduced from (2, 2) space-time

We construct infinite-dimensional symmetries of the two dimensional equation which results from the dimensional reduction of the self-duality condition in (2, 2) signature space-time. These are…

On 2k-Hitchin’s equations and Higgs bundles: A survey

We study the [Formula: see text]-Hitchin’s equations introduced by Ward from the geometric viewpoint of Higgs bundles. After an introduction on Higgs bundles and [Formula: see text]-Hitchin’s…

Minimal surfaces in AdS space and integrable systems

We consider the Pohlmeyer reduction for spacelike minimal area worldsheets in AdS5. The Lax pair for the reduced theory is found, and written entirely in terms of the A3 = D3 root system,…

New Z3 strings

BPS vortices, Q-balls, and Q-vortices in $ \mathcal{N} $ = 6 Chern-Simons matter theory

A bstractWe investigate the vortex-type BPS equations in the ABJM theory without and with mass-deformation. We systematically classify the BPS equations in terms of the number of supersymmetry and…

Infinite dimensional symmetries of self-dual Yang-Mills

We construct symmetries of the Chalmers-Siegel action describing self-dual Yang-Mills theory using a canonical transformation to a free theory. The symmetries form an infinite dimensional Lie algebra…

Deposited in DRO : 17 June 2015 Version of attached le : Other Peer-review status of attached

We construct infinite-dimensional symmetries of the two dimensional equation which results from the dimensional reduction of the self-duality condition in (2, 2) signature space-time. These are…

References

SHOWING 1-10 OF 42 REFERENCES

BPS string solutions in non-Abelian Yang-Mills theories and confinement

Starting from the bosonic part of N=2 Super QCD with a 'Seiberg-Witten' N=2 breaking mass term, we obtain string BPS conditions for arbitrary semi-simple gauge groups. We show that the vacuum…

Construction of exact Riemannian instanton solutions

We present the exact construction of Riemannian (or stringy) instantons, which are classical solutions of 2D Yang–Mills theories that interpolate between initial and final string configurations. They…

Matrix string theory, 2D SYM instantons and affine Toda systems

Heterotic Matrix String Theory and Riemann Surfaces

BPS Z N string tensions, sine law and Casimir scaling, and integrable field theories

We consider a Yang-Mills-Higgs theory with spontaneous symmetry breaking of the gauge group G → U(1) r → C G , with C G being the center of G. We study two vacua solutions of the theory which produce…

Matrix string theory and its moduli space

Z k string fluxes and monopole confinement in non-Abelian theories

Recently (hep-th/0104171) we considered N=2 super Yang-Mills with a N=2 mass breakingn term and showed the existence of BPS Z_{k}-string solutions for arbitrary simple gauge groups which are…

Integrability and Conformal Symmetry in Higher Dimensions: A Model with Exact Hopfion Solutions

We use ideas on integrability in higher dimensions to define Lorentz invariant field theories with an infinite number of local conserved currents. The models considered have a two dimensional target…

Holomorphic reduction of N = 2 gauge theories, Wilson-'t Hooft operators, and S-duality

We study twisted N=2 superconformal gauge theory on a product of two Riemann surfaces Sigma and C. The twisted theory is topological along C and holomorphic along Sigma and does not depend on the…

Self-dual monopoles and toda molecules