Sine–Gordon form factors in finite volume

Abstract

Multi-soliton form factors in sine-Gordon theory from the bootstrap are compared to finite volume matrix elements computed using the truncated conformal space approach. We find convincing agreement, and resolve most of the issues raised in a previous work.

Sine-Gordon multisoliton form factors in finite volume

“…Note that the sign factor (−1) n corresponds to a redefinition of the relative phase between a soliton and an antisoliton. In our previous work [28], it was noticed that such a sign was necessary for a full agreement between the finite size data and the theoretical predictions. Since then we realized that this is explained by the difference between the conventions used for the form factor equations between Lukyanov's work [42] and the finite volume form factor formalism developed in [20,21].…”

“…The formulae for finite volume form factors, derived in [20,21], were generalized for the case of non-diagonal theories in [28]. Here we only recall the necessary facts; for more details the reader is referred to the original papers.…”

“…However, an extension to theories with non-diagonal scattering is still missing. The first steps were taken in [28] with a study of sine-Gordon breather and two-soliton form factors; later the effect of exponential corrections (more specifically so-called µ-terms) was also studied in detail [29]. Even earlier, finite volume breather form factors were already used in studying resonances [30] and form factor perturbation theory [31].…”

“…• In the previous work [28], some issues were left unresolved. These were related to a sign observed in diagonal one-soliton matrix elements, and a numerical discrepancy in the comparison of diagonal matrix elements.…”

“…After a brief review of the necessary facts about sineGordon model in section 2, we recall the formalism for finite volume soliton form factors in section 3. Using the formalism developed in [28], we give theoretical predictions for finite volume matrix elements between multi-soliton states in section 3, which are compared to numerical data from the truncated conformal space approach in section 4. Section 5 is devoted to the conclusions and outlines remaining problems, to be investigated further.…”