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 \( \mathfrak{g} \) 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 \( \mathcal{E} \)-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 \( \mathcal{E} \)-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.
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Acknowledgments
We would like to thank Anders Heide Wallberg and Nat Levine for interesting discussions. The work of FH is supported by the SONATA BIS grant 2021/42/E/ST2/00304 from the National Science Centre (NCN), Polen. The work of SL is supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation. BV gratefully acknowledge the support of the Leverhulme Trust through a Leverhulme Research Project Grant (RPG-2021-154).
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Hassler, F., Lacroix, S. & Vicedo, B. The magic renormalisability of affine Gaudin models. J. High Energ. Phys. 2023, 5 (2023). https://doi.org/10.1007/JHEP12(2023)005
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DOI: https://doi.org/10.1007/JHEP12(2023)005