The magic renormalisability of affine Gaudin models

Abstract

Abstract We study the renormalisation of a large class of integrable σ-models obtained in the framework of affine Gaudin models. They are characterised by a simple Lie algebra g $$ \mathfrak{g} $$ and a rational twist function φ(z) with simple zeros, a double pole at infinity but otherwise no further restrictions on the pole structure. The crucial tool used in our analysis is the interpretation of these integrable theories as E $$ \mathcal{E} $$ -models, which are σ-models studied in the context of Poisson-Lie T-duality and which are known to be at least one- and two-loop renormalisable. The moduli space of E $$ \mathcal{E} $$ -models still contains many non-integrable theories. We identify the submanifold formed by affine Gaudin models and relate its tangent space to curious matrices and semi-magic squares. In particular, these results provide a criteria for the stability of these integrable models under the RG-flow. At one loop, we show that this criteria is satisfied and derive a very simple expression for the RG-flow of the twist function, proving a conjecture made earlier in the literature.

Keywords

• Integrable Field Theories
• Renormalization Group
• Sigma Models
• Field Theories in Lower Dimensions