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arXiv · 2507.02831

Trace Formulas for Deformed W-Algebras

Fabrizio Nieri
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Abstract

We investigate trace formulas in $\varepsilon$-deformed W-algebras, highlighting a novel connection to the modular double of $\mathfrak{q}$-deformed W-algebras. In particular, we show that torus correlators in the additive (Yangian) setting reproduce sphere correlators in the trigonometric setup, possibly with the inclusion of a non-perturbative completion. From a dual perspective, this mechanism implements a gauge theoretic 2d$\to$3d uplift, where a circle direction in the world-sheet transmutes to a compact space-time direction in a non-trivial manner. We further discuss a unified picture of deformed W-algebras driven by trace formulas, suggesting a deeper algebraic layer related to the massive and massless form-factor approach to integrable QFT and 2d CFT.

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Fabrizio Nieri. 2025-07-03. Trace Formulas for Deformed W-Algebras. https://doi.org/10.3842/sigma.2026.003

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