Tailoring Three-Point Functions and Integrability IV. Theta-morphism

TL;DR

This paper introduces the Theta-morphism, an algebraic method to compute higher-loop eigenvectors in N=4 SYM, enabling the calculation of structure constants at one loop with a surprisingly simple final form.

Contribution

The paper develops the Theta-morphism approach to generate higher-loop eigenvectors for arbitrary operators, advancing integrability techniques in N=4 SYM.

Findings

Explicit one-loop structure constants computed using the Theta-morphism.

Proposed all-loop conjectures based on pattern analysis and higher loop experiments.

Simplified expressions for structure constants at one loop.

Abstract

We compute structure constants in N=4 SYM at one loop using Integrability. This requires having full control over the two loop eigenvectors of the dilatation operator for operators of arbitrary size. To achieve this, we develop an algebraic description called the Theta-morphism. In this approach we introduce impurities at each spin chain site, act with particular differential operators on the standard algebraic Bethe ansatz vectors and generate in this way higher loop eigenvectors. The final results for the structure constants take a surprisingly simple form. For some quantities we conjecture all loop generalizations. These are based on the tree level and one loop patterns together and also on some higher loop experiments involving simple operators.