Boundary form factors in finite volume

TL;DR

This paper investigates how boundary field matrix elements depend on volume in quantum field theory, validating the boundary form factor bootstrap through non-perturbative comparisons in the scaling boundary Lee-Yang model.

Contribution

It provides a non-perturbative, direct comparison of exact boundary form factors with matrix elements from the Hamiltonian approach, confirming the bootstrap method's accuracy.

Findings

Solid confirmation of the boundary form factor bootstrap.

Agreement between bootstrap form factors and Hamiltonian matrix elements.

Validation of volume dependence formulas for boundary fields.

Abstract

We describe the volume dependence of matrix elements of local boundary fields to all orders in inverse powers of the volume. Using the scaling boundary Lee-Yang model as testing ground, we compare the matrix elements extracted from boundary truncated conformal space approach to exact form factors obtained using the bootstrap method. We obtain solid confirmation for the boundary form factor bootstrap, which is different from all previously available tests in that it is a non-perturbative and direct comparison of exact form factors to multi-particle matrix elements of local operators, computed from the Hamiltonian formulation of the quantum field theory.