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Modular Properties of mathcal{W}₃ Generalised Gibbs Ensembles
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Modular Properties of mathcal{W}₃ Generalised Gibbs Ensembles
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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.
Forward citations
Cited by 2 Pith papers
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Universal Modular Properties of Generalized Gibbs Ensembles and Chiral Deformations
Modular S-transforms of chirally deformed CFT partition functions are determined iteratively by second-order OPE poles of the deforming currents, with explicit multiplicities.
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Modular Properties of Symplectic Fermion Generalised Gibbs Ensemble
Exact modular S-transforms are derived for GGEs in the symplectic fermion theory, agreeing with conjectures for the W3 zero mode and mirroring free-fermion results for the KdV subset.
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