Integrability of a family of quantum field theories related to sigma models

Date

2011

Authors

Ridout, David
Teschner, Jorg

Journal Title

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Volume Title

Publisher

Elsevier

Abstract

A method is introduced for constructing lattice discretizations of large classes of integrable quantum field theories. The method proceeds in two steps: The quantum algebraic structure underlying the integrability of the model is determined from the algebra of the interaction terms in the light-cone representation. The representation theory of the relevant quantum algebra is then used to construct the basic ingredients of the quantum inverse scattering method, the lattice Lax matrices and R-matrices. This method is illustrated with four examples: The sinh-Gordon model, the affine sl(3) Toda model, a model called the fermionic sl(2|1) Toda theory, and the N=2 supersymmetric sine-Gordon model. These models are all related to sigma models in various ways. The N=2 supersymmetric sine-Gordon model, in particular, describes the Pohlmeyer reduction of string theory on AdS2×S2, and is dual to a supersymmetric non-linear sigma model with a sausage-shaped target space.

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Citation

Source

Nuclear Physics B

Type

Journal article

Book Title

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DOI

10.1016/j.nuclphysb.2011.07.019

Restricted until

2037-12-31