The Magic Renormalisability of Affine Gaudin Models
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arXiv
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| Format: | Preprint |
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2023
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| author | Hassler, Falk Lacroix, Sylvain Vicedo, Benoit |
| author_facet | Hassler, Falk Lacroix, Sylvain Vicedo, Benoit |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_16079 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Magic Renormalisability of Affine Gaudin Models Hassler, Falk Lacroix, Sylvain Vicedo, Benoit High Energy Physics - Theory 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. |
| title | The Magic Renormalisability of Affine Gaudin Models |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2310.16079 |