Quantum Inverse Scattering and the Lambda Deformed Principal Chiral Model

Abstract

The lambda model is a one parameter deformation of the principal chiral model that arises when regularizing the non-compactness of a non-abelian T dual in string theory. It is a current-current deformation of a WZW model that is known to be integrable at the classical and quantum level. The standard techniques of the quantum inverse scattering method cannot be applied because the Poisson bracket is non ultra-local. Inspired by an approach of Faddeev and Reshetikhin, we show that in this class of models, there is a way to deform the symplectic structure of the theory leading to a much simpler theory that is ultra-local and can be quantized on the lattice whilst preserving integrability. This lattice theory takes the form of a generalized spin chain that can be solved by standard algebraic Bethe Ansatz techniques. We then argue that the IR limit of the lattice theory lies in the universality class of the lambda model implying that the spin chain provides a way to apply the quantum inverse scattering method to this non ultra-local theory. This points to a way of applying the same ideas to other lambda models and potentially the string world-sheet theory in the gauge-gravity correspondence.

49 Pages

References in corpus (12)

• On non-abelian T-dual geometries with Ramond fluxes
• On deformations of AdS_n x S^n supercosets
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• Integrable Deformations of Strings on Symmetric Spaces
• Spacetimes for λ-deformations
• Pohlmeyer reduction revisited
• Supergravity background of the lambda-deformed AdS_3 x S^3 supercoset
• The Quantum Deformed Mirror TBA I
• Poisson-Lie T-duals of the bi-Yang-Baxter models
• $\lambda$-deformations of left-right asymmetric CFTs
• Generalized $\lambda$-deformations of AdS_p x S^p
• On the quantization of continuous non-ultralocal integrable systems

Cited by in corpus (12)

• Yang-Baxter and the Boost: splitting the difference
• Classical and Quantum Aspects of Yang-Baxter Wess-Zumino Models
• On the Zakharov-Mikhailov action: $4$d Chern-Simons origin and covariant Poisson algebra of the Lax connection
• RG flow of integrable $\mathcal{E}$-models
• The Faddeev-Reshetikhin model from a 4D Chern-Simons theory
• Ultralocal Lax connection for para-complex ${\mathbb{Z}}_T$-cosets
• Quantum Anisotropic Sigma and Lambda Models as Spin Chains
• Deformed WZW Models and Hodge Theory -- Part I
• Asymptotics in an Asymptotic CFT
• Exceptional solutions to the eight-vertex model and integrability of anisotropic extensions of massive fermionic models
• Scattering in integrable pp-wave backgrounds: S-matrix and absence of particle production
• On the Integrable Structure of the SU(2) Wess-Zumino-Novikov-Witten Model