Trace Formulas for Deformed W-Algebras

2025/07/03 by Nieri, Fabrizio
#FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2507.02831

Abstract

We investigate trace formulas in ε-deformed W-algebras, highlighting a novel connection to the modular double of 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→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.

Citations

• 3-Manifolds and VOA Characters
• Toda 3-Point Functions From Topological Strings
• A_n-Triality
• Gauge/Liouville Triality
• Superconformal Partition Functions and Non-perturbative Topological Strings
• Liouville Correlation Functions from Four-Dimensional Gauge Theories
• The modular properties and the integral representations of the multiple elliptic gamma functions
• Massless XXZ Model and Degeneration of the Elliptic Algebra A_q,p(\widehatsl₂)
• Massless integrable quantum field theories and massless scattering in 1+1 dimensions

Related

• Quadratic relations of the deformed W-algebra
• Trace Relations in Deformed Gauge Theories
• Deformed Double Current Algebras, Matrix Extended \mathcal W_∞ Algebras, Coproducts, and Intertwiners from the M2-M5 Intersection
• Extensions of deformed W-algebras via qq-characters
• The q-AGT-W relations via shuffle algebras