Apor Roth | Searcharxiv

arXiv2026

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

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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arXiv2025

Comparing the elliptic Ruijsenaars-Schneider model to the finite volume sine-Gordon theory

We compare the spectrum of the elliptic Ruijsenaars-Schneider model with the finite-size spectrum of the sine-Gordon model, highlighting both their similarities and differences. Our analysis focuses on the two-particle sector in the center-of-mass frame. At the free point, we carry out an analytic comparison, while at generic couplings we employ non-perturbative numerical calculations based on the truncated Hilbert space method adapted to difference operators. To benchmark this numerical approach, we first study the trigonometric limit, where analytic results are available. We then examine in detail the non-relativistic limit, which encompasses the rational, trigonometric, hyperbolic, and elliptic Calogero-Moser-Sutherland models. Finally, we compare the Bethe-Yang momentum quantization conditions, derived from infinite-volume scattering phases, with the exact finite-volume solutions. We find that these conditions hold exactly in the rational and trigonometric cases, but acquire finite-size corrections in the hyperbolic and elliptic cases, both for the relativistic model and its non-relativistic limit, however, these corrections are different in quantum field theories and in many body systems.

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