• DOI:10.1007/JHEP12(2019)146
• Corpus ID: 203610276

Integrable sigma models and 2-loop RG flow

@article{Hoare2019IntegrableSM,
  title={Integrable sigma models and 2-loop RG flow},
  author={Ben Hoare and Nat Levine and Arkady A. Tseytlin},
  journal={Journal of High Energy Physics},
  year={2019}
}

• B. Hoare, Nat Levine, A. Tseytlin
• Published 1 October 2019
• Mathematics
• Journal of High Energy Physics

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 “λ-model,” an integrable model associated to a group or symmetric space and containing as special limits a (gauged) WZW model and an “interpolating model” for non-abelian 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 λ-model as a σ-model on an extended G × G × G configuration space (g, h,

$$ \overline{h} $$

h
¯

), defining h and

$$ \overline{h} $$

h
¯

by A
+ = h∂+h

−1
, A_ =

$$ \overline{h} $$

h
¯

∂−

$$ \overline{h} $$

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 σ-model found by integrating out A

±
, whose 2-loop 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 2-loop β-function of the λ-model 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 non-abelian dual limit implying that non-abelian duality commutes with the RG flow. We also find the 2-loop β-function of a “squashed” principal chiral model.