Bethe Ansatz and exact form factors of the O (N) Gross Neveu-model

Abstract

We apply previous results on the O(N ) Bethe Ansatz [1-3] to construct a general form factor formula for the O(N ) Gross-Neveu model. We examine this formula for several operators, such as the energy momentum, the spin-field and the current. We also compare these results with the 1/N expansion of this model and obtain full agreement. We discuss bound state form factors, in particular for the three particle form factor of the field. In addition for the two particle case we prove a recursion relation for the K-functions of the higher level Bethe Ansatz.

Algebraic Bethe Ansatz for spinor R-matrices

“…The authors provided explicit examples of spinorspinor R-matrices of low rank and commented on the corresponding cases of the algebraic Bethe ansatz. Similar spectral problems were also addressed by Reshetikhin in [4], De Vega and Karowski in [5], Babujian, Foerster and Karowski in [6,7], Ferrando, Frassek and Kazakov in [8], Liashyk and Pakuliak in [9], and Gerrard together with the author in [10].…”

Algebraic Bethe Ansatz for spinor R-matrices

“…The authors provided explicit examples of spinor-spinor R-matrices of low rank and commented on the corresponding cases of the algebraic Bethe ansatz. Similar spectral problems were also addressed by Reshetikhin in [Rsh85], De Vega and Karowski in [DVK87], Babujian, Foerster and Karowski in [BFK12,BFK16], Ferrando, Frassek and Kazakov in [FFK20], Liashyk and Pakuliak in [LP20], and Gerrard together with the author in [GrR20].…”

Bethe ansatz and exact form factors of theO(6) Gross Neveu-model

“…with the "charge conjugation matrices" C αβ = δ αβ and C αβ = δ αβ (7) in the complex basis (see [11]). The three S-matrix eigenvalues are S…”

“…We introduced an intertwiner, which connects two different S-matrices in the nesting procedure S(θ, N) and S(θ, N − 2). Then we applied this technique in [10] and [11] to the O(N) nonlinear σ-model and the O(N) Gross-Neveu model with even N, respectively. In the present article we will consider the form factors of the O (6) Gross-Neveu model which will be the starting model for the nesting procedure for the O(N) Gross-Neveu model.…”

“…In [10] and [11] we constructed form factors for the O(N) σ-model and the O(N) Gross-Neveu model (for N even), respectively. For these constructions we used the nested Bethe ansatz, which means that for the level N one needs the results from level N − 2 , etc.…”