Form factors of twist fields in the lattice Dirac theory

TL;DR

This paper derives explicit formulas for the form factors of U(1) twist fields in a 2D lattice Dirac fermion model, connecting lattice results to sine-Gordon model form factors at the free-fermion point.

Contribution

It provides the first factorized finite-lattice form factors for U(1) twist fields using elliptic functions and explores their continuum limit relating to sine-Gordon theory.

Findings

Derived finite-lattice form factors using elliptic parametrization.

Connected lattice form factors to sine-Gordon model at free-fermion point.

Analyzed thermodynamic and infinite-volume scaling limits.

Abstract

We study U(1) twist fields in a two-dimensional lattice theory of massive Dirac fermions. Factorized formulas for finite-lattice form factors of these fields are derived using elliptic parametrization of the spectral curve of the model, elliptic determinant identities and theta functional interpolation. We also investigate the thermodynamic and the infinite-volume scaling limit, where the corresponding expressions reduce to form factors of the exponential fields of the sine-Gordon model at the free-fermion point.