Nuclear Phys. B, 2012, Volume 855, Issue 1, Pages 100–127
Haldane limits via Lagrangian embeddings
a Steklov Mathematical Institute, Gubkina str. 8, 119991 Moscow, Russia
b School of Mathematics, Trinity College, Dublin 2, Ireland
In the present paper we revisit the so-called Haldane limit, i.e. a particular continuum limit, which leads from a spin chain to a sigma model. We use the coherent state formulation of the path integral to reduce the problem to a semiclassical one, which leads us to the observation that the Haldane limit is closely related to a Lagrangian embedding into the classical phase space of the spin chain. Using this property, we find a spin chain whose limit produces a relativistic sigma model with target space the manifold of complete flags $U(3)/U(1)^3$. We discuss possible other future applications of Lagrangian/isotropic embeddings in this context.
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