Abstract
Inspired by 5d supersymmetric Yang–Mills theories placed on the compact space {mathbb{S}^5}, we propose an intriguing algebraic construction for the q-Virasoro algebra. We show that, when multiple q-Virasoro “chiral” sectors have to be fused together, a natural {mathrm{SL}(3,mathbb{Z})} structure arises. This construction, which we call the modular triple, is consistent with the observed triple factorization properties of supersymmetric partition functions derived from localization arguments. We also give a 2d CFT-like construction of the modular triple, and conjecture for the first time a (non-local) Lagrangian formulation for a q-Virasoro model, resembling ordinary Liouville theory.
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