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arXiv · 1907.04737

Integrable 2d sigma models: quantum corrections to geometry from RG flow

Ben Hoare·Nat Levine·Arkady A. Tseytlin
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Abstract

Classically integrable $\sigma$-models are known to be solutions of the 1-loop RG equations, or "Ricci flow", with only a few couplings running. In some of the simplest examples of integrable deformations we find that in order to preserve this property at 2 (and higher) loops the classical $\sigma$-model should be corrected by quantum counterterms. The pattern is similar to that of effective $\sigma$-models associated to gauged WZW theories. We consider in detail the examples of the $\eta$-deformation of $S^2$ ("sausage model") and $H^2$, as well as the closely related $\lambda$-deformation of the $SO(1,2)/SO(2)$ coset. We also point out that similar counterterms are required in order for non-abelian duality to commute with RG flow beyond the 1-loop order.

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Ben Hoare, Nat Levine, Arkady A. Tseytlin. 2019-07-10. Integrable 2d sigma models: quantum corrections to geometry from RG flow. https://doi.org/10.1016/j.nuclphysb.2019.114798

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