RG flow of integrable $\mathcal{E}$-models

Abstract

We compute the one- and two-loop RG flow of integrable $\sigma$-models with Poisson-Lie symmetry. They are characterised by a twist function with $2N$ simple poles/zeros and a double pole at infinity. Hence, they capture many of the known integrable deformations in a unified framework, which has a geometric interpretation in terms of surface defects in a 4D Chern-Simons theory. We find that these models are one-loop renormalisable and present a very simple expression for the flow of the twist function. At two loops only models with $N$=1 are renormalisable. Applied to the $\lambda$-deformation on a semisimple group manifold, our results reproduce the $\beta$-functions in the literature.

7 pages

References in corpus (6)

• Abelian Yang-Baxter Deformations and TsT transformations
• Background Field Equations for the Duality Symmetric String
• The all-loop non-Abelian Thirring model and its RG flow
• Quantum correction to generalized T-dualities
• ${\alpha }^{\prime }$-corrected Poisson-Lie T-duality
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Cited by in corpus (9)

• Integrable Deformations of Sigma Models
• O(D,D) and the string ${\alpha }^{\prime }$ expansion: An obstruction
• 4-dimensional Chern-Simons theory and integrable field theories
• Sigma models as Gross-Neveu models
• Universal 1-loop divergences for integrable sigma models
• An elliptic integrable deformation of the Principal Chiral Model
• Geometry of the spectral parameter and renormalisation of integrable $\sigma$-models
• The Magic Renormalisability of Affine Gaudin Models
• Point particle E-models