Integrable properties of sigma-models with non-symmetric target spaces

Abstract

It is well-known that sigma-models with symmetric target spaces are classically integrable. At the example of the model with target space the flag manifold U(3)/U(1)^3 -- a non-symmetric space -- we show that the introduction of torsion allows to cast the equations of motion in the form of a zero-curvature condition for a one-parametric family of connections, which can be a sign of integrability of the theory. We also elaborate on geometric aspects of the proposed model.

arXiv comment8 pages, 1 figure

References in corpus (4)

• Strings on Semisymmetric Superspaces
• Superisometries and integrability of superstrings
• Haldane limits via Lagrangian embeddings
• Heterotic strings on homogeneous spaces

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• BPS Sphalerons in the $F_2$ Non-Linear Sigma Model
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• Lax pairs for new ${\mathbb{Z}}_N$-symmetric coset $\sigma$-models and their Yang-Baxter deformations
• The classical and quantum particle on a flag manifold
• Scale without conformal invariance from integrable deformations of coset CFTs
• Notes on index of quantum integrability