Modular Properties of $\mathcal{W}_3$ Generalised Gibbs Ensembles
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909748966719488 |
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| author | Downing, Max Karimi, Faisal Sengupta, Tanmoy Sudhakar, Adarsh Watts, Gérard M T |
| author_facet | Downing, Max Karimi, Faisal Sengupta, Tanmoy Sudhakar, Adarsh Watts, Gérard M T |
| contents | In this paper we make a proposal for the solution to a long-standing problem - the asymptotic expansions of the modular $S$-transform of a generalised Gibbs ensemble (GGE) in a theory with $\mathcal{W}_3$ symmetry where the GGE includes the first non-trivial charge. Equivalently, we give a proposal for the modular $S$-transform of traces of arbitrary powers of the zero mode $W_0$. We provide evidence in the form of exact results using Zhu's recursion, results obtained using conjectured results for Verma modules, and exact results for the particular value $c=-2$. We expect these have generalisations to other symmetry algebras/hierarchies such as the Virasoro algebra/KdV charges, and to GGEs with arbitrary finite sets of charges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16258 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modular Properties of $\mathcal{W}_3$ Generalised Gibbs Ensembles Downing, Max Karimi, Faisal Sengupta, Tanmoy Sudhakar, Adarsh Watts, Gérard M T High Energy Physics - Theory Statistical Mechanics Mathematical Physics In this paper we make a proposal for the solution to a long-standing problem - the asymptotic expansions of the modular $S$-transform of a generalised Gibbs ensemble (GGE) in a theory with $\mathcal{W}_3$ symmetry where the GGE includes the first non-trivial charge. Equivalently, we give a proposal for the modular $S$-transform of traces of arbitrary powers of the zero mode $W_0$. We provide evidence in the form of exact results using Zhu's recursion, results obtained using conjectured results for Verma modules, and exact results for the particular value $c=-2$. We expect these have generalisations to other symmetry algebras/hierarchies such as the Virasoro algebra/KdV charges, and to GGEs with arbitrary finite sets of charges. |
| title | Modular Properties of $\mathcal{W}_3$ Generalised Gibbs Ensembles |
| topic | High Energy Physics - Theory Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2508.16258 |