Integrability vs. RG flow in $G\times G$ and $G\times G/H$ sigma models

Abstract

We consider a class of 2d $\sigma$-models on products of group spaces that provide new examples of a close connection between integrability and stability under the RG flow. We first study the integrable $G\times G$ model derived from the affine Gaudin construction (for which the 1-loop $\beta$-functions were found in arXiv:2010.07879) and show that its condition of integrability is preserved also by the 2-loop RG flow. We then investigate the RG flow in the gauged $G\times G/H$ model, in particular the integrable $T^{1,1}$ model found in arXiv:2010.05573. We also construct a new class of integrable $G\times G/H$ models in the case when the subgroup $H$ is abelian. In the simplest case of $G=S{U}_2$, $H=U_1$ this leads to an integrable $\sigma$-model on the $T^{1,q}$ space (with a particular $B$-field). This model is also shown to be stable under the 2-loop RG flow, and we relate this property to its invariance under T-duality in an isometric $U_1$ direction. This $T^{1,q}$ model may be interpreted as an integrable deformation of the GMM model (of two coupled WZW theories with generic levels) away from the conformal point.

arXiv comment26 pages, supplementary Mathematica file; v5: minor corrections

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Cited by in corpus (7)

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• Universal 1-loop divergences for integrable sigma models
• Geometry of the spectral parameter and renormalisation of integrable $\sigma$-models
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• Integrable sigma models on Riemann surfaces