Abstract
The 6-vertex model with appropriately chosen alternating inhomogeneities gives the so-called light-cone lattice regularization of the sine-Gordon (Massive-Thirring) model. In this integrable lattice model we consider pure hole states above the antiferromagnetic vacuum and express the norm of Bethe-wave functions in terms of the hole's positions and the counting-function of the state under consideration. In the light-cone regularized picture pure hole states correspond to pure soliton (fermion) states of the sine-Gordon (massive Thirring) model. Hence, we analyze the continuum limit of our new formula for the norm of the Bethe-wave functions. We show, that the physically most relevant determinant part of our formula can be expanded in the large volume limit and turns out to be proportional to the Gaudin-determinant of pure soliton states in the sine-Gordon model defined in finite volume.
Highlights
Finite volume form-factors in integrable quantum field theories attract interest because of their relevance in the solution of the planar AdS/CFT correspondence [1, 2].There are two basic approaches to finite volume form-factors in integrable quantum field theories
The first approach initiated in [3, 4] describes the finite volume form-factors in the form of a large volume series built from the infinite volume form-factors [15] of the theory
We investigate the continuum limit of the Gaudin-determinant detΦ and show that its most complicated determinant part is proportional to a product of two determinants
Summary
Finite volume form-factors in integrable quantum field theories attract interest because of their relevance in the solution of the planar AdS/CFT correspondence [1, 2]. The second approach based on an integrable lattice regularization of the quantum field theory under consideration, led to remarkable results in the sine-Gordon (MassiveThirring) model In this framework finite volume 1-point functions [10, 11], ratios of infinite volume form-factors [12] and the diagonal finite volume solitonic matrix elements of the U (1) current [17] and the trace of the stress-energy tensor [18] have been determined. In this paper we consider the simplest determinant arising in the light-cone lattice regulrization [19] based computation of non-diagonal form-factors in the sine-Gordon (massive Thirring) model This is the so-called Gaudin-determinant detΦ, which determines the norm square of a Bethe-eigenstate |λ (2.6) through the formula [33, 34, 35]:. The paper contains two appendices, in which some formulas being helpful for the computations of the paper are collected
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