ODE/IM correspondence for the Fateev model
Abstract
The Fateev model is somewhat special among twodimensional quantum field theories. For different values of the parameters, it can be reduced to a variety of integrable systems. An incomplete list of the reductions includes O(3) and O(4) nonlinear sigma models and their continuous deformations (2D and 3D sausages, anisotropic principal chiral field), the BukhvostovLipatov model, the N = 2 supersymmetric sineGordon model, as well as the integrable perturbed SU _{2}( n) ⊗ SU _{2}( p  2) /SU _{2}( n + p  2) coset CFT. The model possesses a mysterious symmetry structure of the exceptional quantum superalgebras U _{ q } ((21; α)). In this work, we propose the ODE/IM correspondence between the Fateev model and a certain generalization of the classical problem of constant mean curvature embedding of a thricepunctured sphere in AdS _{3}.
 Publication:

Journal of High Energy Physics
 Pub Date:
 December 2013
 DOI:
 10.1007/JHEP12(2013)012
 arXiv:
 arXiv:1303.2566
 Bibcode:
 2013JHEP...12..012L
 Keywords:

 Field Theories in Lower Dimensions;
 Integrable Hierarchies;
 Integrable Field Theories;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 28 pages, 4 figures