We revisit the analysis of the integrated 2-point functions of local operators with a 1/2-BPS Wilson line in N=4 SYM. After including suitable parity-odd terms in the parametrization of the defect correlators, we are able to solve the superconformal Ward identities in terms of an unconstrained function of the cross-ratios. Exploiting this general solution, we obtain a simple expression of the integration measure for the integrated correlators with a Wilson line. We test our result by integrating the available bootstrap expression of the unintegrated correlator at strong coupling against the predictions of supersymmetric localization, finding perfect agreement.
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Billó et al. (2024) studied this question.
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