Integrable Nonlinear $\sigma$ Models With Fermions

Abdalla, E.; Forger, M.

doi:10.1007/BF01210796

Integrable Nonlinear $\sigma$ Models With Fermions

E. Abdalla
(
- Sao Paulo U.
)
,
M. Forger
(
- CERN
)

Jul, 1985

40 pages

Published in:

Commun.Math.Phys. 104 (1986) 123

DOI:

10.1007/BF01210796

Report number:

CERN-TH-4238/85

View in:

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Abstract: (Springer)

The two-dimensional non-linear σ model on a Riemannian symmetric spaceM=G/H is coupled to fermions with quartic self-interactions. The resulting hybrid model is presented in a gauge-dependent formulation, with a bosonic field taking values inG and a fermionic field transforming under a given representation of the gauge groupH. General criteria for classical integrability are presented: they essentially fix the Lagrangian of the model but leave the fermion representation completely arbitrary. It is shown that by a special choice for the fermion representation (derived from the adjoint representation ofG by an appropriate reduction) one arrives naturally at the supersymmetric non-linear σ model onM=G/H. The issue of quantum integrability is also discussed, though with less stringent results.

FIELD THEORETICAL MODEL: SIGMA
NONLINEAR
FERMION: REPRESENTATION
FIELD THEORY: TWO-DIMENSIONAL
SUPERSYMMETRY
FIELD EQUATIONS: SOLUTION
CHARGE: NONLOCAL
MATHEMATICAL METHODS: DIFFERENTIAL GEOMETRY

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