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.

26 pages, supplementary Mathematica file; v5: minor corrections

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Cited by in corpus (7)

• Integrable supersymmetric deformations of $\mathrm{Ad}{\mathrm{S}}_3\times {\mathrm{S}}^3\times {\mathrm{T}}^4$
• Universal 1-loop divergences for integrable sigma models
• Geometry of the spectral parameter and renormalisation of integrable $\sigma$-models
• On loop corrections to integrable $2D$ sigma model backgrounds
• Integrable deformed $T^{1,1}$ sigma models from 4D Chern-Simons theory
• The Magic Renormalisability of Affine Gaudin Models
• Integrable sigma models on Riemann surfaces