Integrable sigma models and 2-loop RG flow
Oct 1, 2019
28 pages
Published in:
- JHEP 12 (2019) 146
- Published: Dec 20, 2019
e-Print:
- 1910.00397 [hep-th]
Report number:
- Imperial-TP-AT-2019-06
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Abstract: (Springer)
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,), defining h and by A = h∂+h^{−}^{1}, A_ = ∂− \overline{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.Note:
- 28 pages; v3: minor comments and references added
- Integrable Field Theories
- Renormalization Group
- Sigma Models
- renormalization group: flow
- model: integrability
- deformation
- Wess-Zumino-Witten model
- renormalizable
- sigma model
- dimension: 2
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