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Abstract
We review the recently proposed class of σ-models with complex homogeneous target spaces, whose equations of motion admit zero-curvature representations.
Highlights
Its critical points X(z, z) are called harmonic maps
We will be interested in the case when the target space M is homogeneous: M = G/H, G compact and semi-simple
Since the group G acts transitively on its quotient space G/H, the equations of motion are equivalent to the conservation of the current
Summary
Its critical points X(z, z) are called harmonic maps. We will be interested in the case when the target space M is homogeneous: M = G/H, G compact and semi-simple. The action of a σ-model with homogeneous target space G/H is globally invariant under the Lie group G. It was observed by Pohlmeyer [1] that in the case when the target space is symmetric, the current K is, flat (when viewed as a one-form and with proper normalization): dK − K ∧ K = 0 (5)
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