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The massive harmonic explorer is a model of random discrete path on thehexagonal lattice that was proposed by Makarov and Smirnov as a massiveperturbation of the harmonic explorer. They argued that the scaling limit ofthe massive harmonic explorer in a bounded domain is a massive version ofchordal SLE$_4$, called massive SLE$_4$, which is conformally covariant andabsolutely continuous with respect to chordal SLE$_4$. In this paper, weprovide a full and rigorous proof of this statement. Moreover, we show that amassive SLE$_4$ curve can be coupled with a massive Gaussian free field as itslevel line, when the field has appropriate boundary conditions.

Massive SLE$_4$ and the scaling limit of the massive harmonic explorer