Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 21 (2025), 010, 21 pages      arXiv:2312.15522      https://doi.org/10.3842/SIGMA.2025.010

Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States II

Sergei Adler and Hermann Boos
Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, 42097 Wuppertal, Germany

Received July 03, 2024, in final form February 07, 2025; Published online February 16, 2025

Abstract
We consider the XXZ spin chain in the scaling limit in the Matsubara direction. The main result of this paper is new representations for the functions $\Psi(l, \kappa)$ and $\Theta(l, m; \kappa, \alpha)$ associated with the function $\omega(\zeta, \xi; \kappa, \kappa)$ found in the expression for the correlation function of the generators of the fermionic basis for the XXZ spin chain. The final result incorporates the case of particle-hole excitations which is needed for the relation of the fermionic basis to the Virasoro basis of the CFT descendants.

Key words: integrable models; six-vertex model; XXZ spin chain; thermodynamic Bethe ansatz; fermionic basis; excited states; conformal field theory; Virasoro algebra.

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