Boundary form factors in the Smirnov--Fateev model with a diagonal boundary $S$ matrix

TL;DR

This paper investigates boundary form factors in the Smirnov--Fateev model with diagonal boundary S-matrix, revealing that free field representation restricts solutions to a finite set, contrasting with the sine-Gordon case.

Contribution

It demonstrates how free field representation constrains boundary S-matrices in the Smirnov--Fateev model, limiting solutions to a finite set.

Findings

Free field representation imposes severe restrictions on boundary S-matrix solutions.

Only a finite number of solutions are consistent with the free field realization.

Contrasts the boundary conditions in the Smirnov--Fateev model with those in the sine-Gordon model.

Abstract

The boundary conditions with diagonal boundary $S$ matrix and the boundary form factors for the Smirnov--Fateev model on a half line has been considered in the framework of the free field representation. In contrast to the case of the sine-Gordon model, in this case the free field representation is shown to impose severe restrictions on the boundary $S$ matrix, so that a finite number of solutions is only consistent with the free field realization.