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)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
