Operator-algebraic construction of the deformed Sine-Gordon model

TL;DR

This paper constructs a deformed Sine-Gordon quantum field theory with bound states using operator-algebraic methods, introducing wedge-local fields and a bound state operator to extend previous models.

Contribution

It extends the operator-algebraic construction of integrable quantum field theories to include models with bound states, specifically a deformed Sine-Gordon model with breathers.

Findings

Constructed wedge-local fields for the deformed Sine-Gordon model.

Introduced a bound state operator to account for poles in the S-matrix.

Extended the operator-algebraic approach to models with bound states.

Abstract

We consider the construction of integrable quantum field theories in the operator-algebraic approach, which is based on quantum fields localized in infinitely extended wedge regions. This approach has been successful for the construction of a class of models with scalar $S$-matrices and without bound states. In extension of these results, we apply similar methods to $S$-matrices with poles in the physical strip (``bound states''). Specifically, we consider a deformed version of the Sine-Gordon model, containing only breathers. We exhibit wedge-local fields in this model, which differ from those in non-bound state models by an additive term, the so called ``bound state operator''.