Integrable sigma models and 2loop RG flow
Abstract
Following arXiv:1907.04737, we continue our investigation of the relation between the renormalizability (with finitely many couplings) and integrability in 2d σ models. We focus on the "λmodel," an integrable model associated to a group or symmetric space and containing as special limits a (gauged) WZW model and an "interpolating model" for nonabelian duality. The parameters are the WZ level k and the coupling λ, and the fields are g, valued in a group G, and a 2d vector A± in the corresponding algebra. We formulate the λmodel as a σmodel on an extended G × G × G configuration space (g, h,h ¯), defining h and h ¯ by A_{+} = h∂+h^{1}, A_ = h ¯∂h ¯^{1}. Our central observation is that the model on this extended configuration space is renormalizable without any deformation, with only λ running. This is in contrast to the standard σmodel found by integrating out A_{±}, whose 2loop renormalizability is only obtained after the addition of specific finite local counterterms, resulting in a quantum deformation of the target space geometry. We compute the 2loop βfunction of the λmodel for general group and symmetric spaces, and illustrate our results on the examples of SU(2)/U(1) and SU(2). Similar conclusions apply in the nonabelian dual limit implying that nonabelian duality commutes with the RG flow. We also find the 2loop βfunction of a "squashed" principal chiral model.
 Publication:

Journal of High Energy Physics
 Pub Date:
 December 2019
 DOI:
 10.1007/JHEP12(2019)146
 arXiv:
 arXiv:1910.00397
 Bibcode:
 2019JHEP...12..146H
 Keywords:

 Integrable Field Theories;
 Renormalization Group;
 Sigma Models;
 High Energy Physics  Theory
 EPrint:
 28 pages