The magic renormalisability of affine Gaudin models
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2023-12-01
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Journal Article
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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 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-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-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.
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published
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2023 (12)
Pages / Article No.
5
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Springer
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Subject
Integrable field theories; Renormalization group; Sigma models; Field theories in lower dimensions
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02889 - ETH Institut für Theoretische Studien / ETH Institute for Theoretical Studies