Diagonal form factors and hexagon form factors

TL;DR

This paper proves a key conjecture about the polynomial dependence of heavy-heavy-light structure constants in N=4 super-Yang-Mills theory, using the hexagon bootstrap approach, and discusses finite-size corrections.

Contribution

It provides a proof of the polynomial L-dependence conjecture for HHL structure constants, extending the hexagon bootstrap method to finite-size effects.

Findings

Confirmed polynomial L-dependence of HHL structure constants

Derived leading finite-size corrections

Validated the hexagon bootstrap approach for specific setups

Abstract

We study the heavy-heavy-light (HHL) three-point functions in the planar N = 4 super-Yang- Mills theory using the recently proposed hexagon bootstrap program [arXiv:1505.06745]. We prove the conjecture of Bajnok, Janik and Wereszczynski [arXiv:1404.4556] on the polynomial L-dependence of HHL structure constant up to the leading finite-size corrections, where L is the length of the heavy operators. The proof is presented for a specific set-up but the method can be applied to more general situations.