Integrable Generalized Principal Chiral Models

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.

14 pages, harvmac (l)

References in corpus (4)

• Irrational Conformal Field Theory
• Comments on Two-Loop Kac-Moody Algebras
• Integrable Generalized Thirring Model
• The Conformal Points of the Generalized Thirring Model II

Cited by in corpus (16)

• On integrability of the Yang-Baxter $\si$-model
• On (non)integrability of classical strings in p-brane backgrounds
• On the geometry of classically integrable two-dimensional non-linear sigma models
• $G$-Strands
• Integrable Generalized Thirring Model
• Improvement of a conserved current density versus adding a total derivative to a Lagrangian density
• On some integrable deformations of the Wess-Zumino-Witten model
• Classical Integrability of Two Dimensional Non Linear Sigma Models
• $G$-Strands and Peakon Collisions on $\mathrm{Diff}(\mathbb{R})$
• Principal models on a solvable group with nonconstant metric
• Integrable sigma models with complex and generalized complex structures
• All generalized SU(2) chiral models have spectral dependent Lax formulation
• Integrable sigma model with generalized $\mathcal{F}$ structure, Yang-Baxter sigma model with generalized complex structure and multi-Yang-Baxter sigma model
• Integrable deformed H${}_{{}_4}$ WZW models and their non-Abelian duals as solutions of generalized supergravity equations
• Towards the Lax formulation of SU(2) principal models with nonconstant metric
• Integrable sigma models with Haantjes structure on $H_4$ Lie group