Polynomial Recursion Equations in Form Factors of ADE Toda Field Theories

TL;DR

This paper presents a recursive polynomial approach to calculating form factors in ADE affine Toda field theories, linking Lie algebra structures with symmetric group representations for explicit solutions.

Contribution

It introduces explicit recursion equations for form factors in ADE Toda theories, connecting Lie algebra weight spaces with symmetric group representations.

Findings

Derived explicit recursion equations for ADE form factors

Characterized polynomial solutions via Lie algebra and symmetric group interplay

Provided a nonperturbative recursive method for form factor calculations

Abstract

It is shown that the problem of calculating form factors in ADE affine Toda field theories can be reduced to the nonperturbative recursive calculation of polynomials symmetric in each sort of variables. We determine these recursion equations explicitly for the ADE series and characterize the polynomial solutions by an interplay between the weight space of the underlying Lie algebra and representations of the symmetric group.