Classification of non-Abelian Chern-Simons vortices

dimensional gauged nonlinear Schrödinger equation with Chern-Simons matter-gauge coupling. The finite charge vacuum states in the Chern-Simons theory are shown to be gauge equivalent to the finite action solutions to the two-dimensional chiral model (or harmonic map) equations. The Uhlenbeck-Wood classification of such harmonic maps into the unitary groups thereby leads to a complete classification of the vacuum states of the Chern-Simons model. This construction also leads to an interesting new relationship between

SU(N)

Toda theories and the

SU(N)

chiral model.

talk: Ixtapa 1993/09
gauge field theory: SU(N)
dimension: 3
field equations: vortex
duality
Chern-Simons term

References(16)

Figures(0)

Selfdual Chern-Simons solitons with noncompact groups

D. Cangemi
(
- MIT, LNS
)

- J.Phys.A 26 (1993) 2945-2954
•
e-Print:
- hep-th/9204008
•
DOI:
- 10.1088/0305-4470/26/12/030

Properties of General Classical {CP} $^{(n-1)}$ Solutions

A.M. Din
(
- Annecy, LAPP
)
,
W.J. Zakrzewski
(
- Durham U.
)

- Phys.Lett.B 95 (1980) 419-422
•
DOI:
- 10.1016/0370-2693(80)90181-1

Interpretation and Further Properties of General Classical {CP} $^{(n-1)}$ Solutions

A.M. Din
(
- Annecy, LAPP
)
,
W.J. Zakrzewski
(
- Durham U.
)

- Nucl.Phys.B 182 (1981) 151-157
•
DOI:
- 10.1016/0550-3213(81)90463-6

Selfdual Chern-Simons solitons and two-dimensional nonlinear equations

- Phys.Rev.D 43 (1991) 1332,
- Phys.Rev.D 45 (1992) 3012 (erratum)
•
DOI:
- 10.1103/PhysRevD.43.1332

Chern-Simons solitons, toda theories and the chiral model

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

- Commun.Math.Phys. 150 (1992) 519-535,
- Commun. Math. Phys. 150 (1992) 519-535 and MIT Cambridge - CTP-2079 (92/03,rec.May) 19 p
•
e-Print:
- hep-th/9204056
•
DOI:
- 10.1007/BF02096959

Hierarchy of soliton solutions to the gauged nonlinear Schrodinger equation on the plane

Bernard Grossman
(
- Princeton, Inst. Advanced Study and
- LLNL, Livermore
)

- Phys.Rev.Lett. 65 (1990) 3230-3232
•
DOI:
- 10.1103/PhysRevLett.65.3230

Soliton Solutions to the Gauged Nonlinear Schrodinger Equation on the Plane

R. Jackiw
(
- Columbia U.
)
,
S.Y. Pi
(
- Rockefeller U.
)

- Phys.Rev.Lett. 64 (1990) 2969-2972
•
DOI:
- 10.1103/PhysRevLett.64.2969

Classical and quantal nonrelativistic Chern-Simons theory

R. Jackiw
(
- Columbia U.
)
,
So-Young Pi
(
- Rockefeller U.
)

- Phys.Rev.D 42 (1990) 3500,
- Phys.Rev.D 48 (1993) 3929 (erratum)
•
DOI:
- 10.1103/PhysRevD.42.3500

The Solution to a generalized Toda lattice and representation theory

Bertram Kostant
(
- MIT
)

- Adv.Math. 34 (1979) 195-338
•
DOI:
- 10.1016/0001-8708(79)90057-4

- Lett.Math.Phys. 3 389

Representation Theory and Integration of Nonlinear Spherically Symmetric Equations to Gauge Theories

A.N. Leznov
(
- Serpukhov, IHEP
)
,
M.V. Saveliev
(
- Serpukhov, IHEP
)

- Commun.Math.Phys. 74 (1980) 111-118,
- In * Zvenigorod 1979, Proceedings, Group Theoretical Methods In Physics, Vol. 2*, 308-316
•
DOI:
- 10.1007/BF01197753

- J.Math.Pure.Appl. 18 71

- J.Diff.Geom. 30 1

- Topology 27 129

Classical solutions of the chiral model, unitons, and holomorphic vector bundles

R.S. Ward
(
- Durham U.
)

- Commun.Math.Phys. 128 (1990) 319-332
•
DOI:
- 10.1007/BF02108784

- Proc.Lond.Math.Soc. 58 608