Chern-Simons solitons, toda theories and the chiral model

Dunne, Gerald V.

doi:10.1007/BF02096959

Chern-Simons solitons, toda theories and the chiral model

Gerald V. Dunne
(
- MIT and
- MIT, LNS
)

Mar, 1992

19 pages

Published in:

Commun.Math.Phys. 150 (1992) 519-535

e-Print:

hep-th/9204056 [hep-th]

DOI:

10.1007/BF02096959

Report number:

MIT-CTP-2079

View in:

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Abstract:

The two-dimensional self-dual Chern--Simons equations are equivalent to the conditions for static, zero-energy solutions of the

(2+1)

-dimensional gauged nonlinear Schr\"odinger equation with Chern--Simons matter-gauge dynamics. In this paper we classify all finite charge

SU(N)

solutions by first transforming the self-dual Chern--Simons equations into the two-dimensional chiral model (or harmonic map) equations, and then using the Uhlenbeck--Wood classification of harmonic maps into the unitary groups. This construction also leads to a new relationship between the

SU(N)

Toda and

SU(N)

chiral model solutions.

Schroedinger equation: nonlinear
gauge field theory: Yang-Mills
Chern-Simons term
field equations: solution
field equations: Toda
duality
symmetry: SU(N)
model: chiral
dimension: 3

References(27)

Figures(0)

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