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 Nuclear Phys. B, 2012, Volume 855, Issue 1, Pages 100–127 (Mi nphb12)

Haldane limits via Lagrangian embeddings

D. Bykovab

a Steklov Mathematical Institute, Gubkina str. 8, 119991 Moscow, Russia
b School of Mathematics, Trinity College, Dublin 2, Ireland

Abstract: 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.

 Funding Agency Grant Number Russian Foundation for Basic Research 11-01-00296-a11-01-12037-ofi-m Ministry of Education and Science of the Russian Federation NSh-8265.2010.1 Irish Research Council My work was supported by the Irish Research Council for Science, Engineering and Technology, in part by grants RFBR 11-01-00296-a, 11-01-12037-ofi-m-2011 and in part by grant for the Support of Leading Scientific Schools of Russia NSh-8265.2010.1.

DOI: https://doi.org/10.1016/j.nuclphysb.2011.10.005

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Document Type: Article
Revised: 02.10.2011
Accepted:06.10.2011
Language: English