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arXiv · 2606.20018

Leading UV Formula for Finite-Volume Vertex Operator Expectation Values in the Sine-Gordon Model from Kink NLIE

Arpad Hegedus·Apor Roth
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Abstract

We study the ultraviolet (UV) limit of finite-volume expectation values of vertex operators in the sine-Gordon model using the kink nonlinear integral equation (NLIE) description of the conformal limit. By analysing the integrable formulation of vacuum expectation values in the small-volume regime, we conjecture an explicit analytic expression for the leading asymptotic term in the small-volume expansion, formulated in terms of kink functions. This establishes a direct connection between the integrable finite-volume description and the expected conformal asymptotics determined by the 3-point functions of the underlying conformal field theory (CFT). The proposed formula is tested against the analytic expression known from complex Liouville conformal field theory using high-precision numerics, showing agreement to at least 19 significant digits.

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Arpad Hegedus, Apor Roth. 2026-06-18. Leading UV Formula for Finite-Volume Vertex Operator Expectation Values in the Sine-Gordon Model from Kink NLIE. https://arxiv.org/abs/2606.20018

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