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

TL;DR

This paper extends the fermionic basis framework to excited states in the six-vertex model, establishing a link with conformal field theory correlation functions and employing the excited-state TBA approach for detailed analysis.

Contribution

It generalizes the fermionic basis to excited states and connects lattice model excitations with conformal field theory using the excited-state TBA.

Findings

Established equivalence between scaled partition functions and CFT correlators.

Extended fermionic basis to include excitations, specifically analyzing level 8 descendants.

Linked lattice model excitations with conformal descendants via TBA.

Abstract

We generalize the results of [Comm. Math. Phys. 299 (2010), 825-866, arXiv:0911.3731] (hidden Grassmann structure IV) to the case of excited states of the transfer matrix of the six-vertex model acting in the so-called Matsubara direction. We establish an equivalence between a scaling limit of the partition function of the six-vertex model on a cylinder with quasi-local operators inserted and special boundary conditions, corresponding to particle-hole excitations, on the one hand, and certain three-point correlation functions of conformal field theory (CFT) on the other hand. As in hidden Grassmann structure IV, the fermionic basis developed in previous papers and its conformal limit are used for a description of the quasi-local operators. In paper IV we claimed that in the conformal limit the fermionic creation operators generate a basis equivalent to the basis of the descendant states in the conformal field theory modulo integrals of motion suggested by A. Zamolodchikov (1987). Here we argue that, in order to completely determine the transformation between the above fermionic basis and the basis of descendants in the CFT, we need to involve excitations. On the side of the lattice model we use the excited-state TBA approach. We consider in detail the case of the descendant at level 8.