Diagonal Form Factors and Heavy-Heavy-Light Three-Point Functions at Weak Coupling

TL;DR

This paper investigates the volume dependence of heavy-heavy-light three-point functions in N=4 SYM at weak coupling, confirming a conjectured form at one-loop level and linking finite volume results to infinite volume form factors.

Contribution

It provides the first explicit weak coupling calculation of the volume dependence of HHL correlators, validating a conjecture about their form and connecting finite and infinite volume form factors.

Findings

Finite volume dependence matches the conjectured form at one-loop.

The computation links finite volume correlators to infinite volume form factors.

Results support the universality of the volume dependence across coupling regimes.

Abstract

In this paper we consider a special kind of three-point functions of HHL type at weak coupling in N=4 SYM theory and analyze its volume dependence. At strong coupling this kind of three-point functions were studied recently by Bajnok, Janik and Wereszczynski [1]. The authors considered some cases of HHL correlator in the su(2) sector and, relying on their explicit results, formulated a conjecture about the form of the volume dependence of the symmetric HHL structure constant to be valid at any coupling up to wrapping corrections. In order to test this hypothesis we considered the HHL correlator in su(2) sector at weak coupling and directly showed that, up to one loop, the finite volume dependence has exactly the form proposed in [1]. Another side of the conjecture suggests that computation of the symmetric structure constant is equivalent to computing the corresponding set of infinite volume form factors, which can be extracted as the coefficients of finite volume expansion. In this sense, extracting appropriate coefficients from our result gives a prediction for the corresponding infinite volume form factors.