Cutting the cylinder into squares: The square form factor

TL;DR

This paper introduces a 'square form factor' method for constructing two-point functions, deriving constraints that lead to the reconstruction of the Gaudin determinant and computing Bethe state norms.

Contribution

It proposes a novel square form factor approach inspired by the hexagon proposal, enabling new calculations of Gaudin determinants and Bethe state norms.

Findings

Derived a consistency condition constraining square form factors.

Reconstructed the Gaudin determinant via forest expansion.

Computed norms of off-shell Bethe states for specific cases.

Abstract

In this article we present a method for constructing two-point functions in the spirit of the hexagon proposal, which leads us to propose a "square form factor". Since cutting the square gives us two squares, we can write a consistency condition that heavily constrains such form factors. In particular, we are able to use this constraint to reconstruct the Gaudin through the forest expansion of the determinant appearing in its definition. We also use this procedure to compute the norm of off-shell Bethe states for some simple cases.