On the boundary form factor program

TL;DR

This paper derives boundary form factor axioms for integrable 1+1D quantum field theories, constructs minimal solutions for several models, and verifies their consistency with known exact and conformal data.

Contribution

It introduces boundary form factor axioms for local boundary operators and provides explicit minimal solutions for multiple integrable models, confirming their validity.

Findings

Boundary form factor axioms are successfully derived.

Minimal solutions match the number of local operators in free models.

Calculated two-point functions agree with exact and conformal results.

Abstract

Boundary form factor axioms are derived for the matrix elements of local boundary operators in integrable 1+1 dimensional boundary quantum field theories using the analyticity properties of correlators via the boundary reduction formula. Minimal solutions are determined for the integrable boundary perturbations of the free boson, free fermion (Ising), Lee-Yang and sinh-Gordon models and the two point functions calculated from them are checked against the exact solutions in the free cases and against the conformal data in the ultraviolet limit for the Lee-Yang model. In the case of the free boson/fermion the dimension of the solution space of the boundary form factor equation is shown to match the number of independent local operators. We obtain excellent agreement which proves not only the correctness of the solutions but also confirms the form factor axioms.