Integrable generalized principal chiral models

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Abstract

We study 2D non-linear sigma models on a group manifold with a special form of the metric. We address the question of integrability for this special class of sigma models. We derive two algebraic conditions for the metric on the group manifold. Each solution of these conditions defines an integrable model. Although the algebraic system is overdetermined in general, we give two examples of solutions. We find the Lax field for these models and calculate their Poisson brackets. We also obtain the renormalization group (RG) equations, to first order, for the generic model. We solve the RG equations for the examples we have and show that they are integrable along the RG flow.

Original languageEnglish
Pages (from-to)374-380
Number of pages7
JournalPhysics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume391
Issue number3-4
DOIs
StatePublished - 16 Jan 1997
Externally publishedYes

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