  We study local operator insertions on 1/2-BPS line defects in ABJM theory.
Specifically, we consider a class of four-point correlators in the CFT$_1$ with
SU$(1, 1|3)$ superconformal symmetry defined on the 1/2-BPS Wilson line. The
relevant insertions belong to the short supermultiplet containing the
displacement operator and correspond to fluctuations of the dual fundamental
string in AdS$_4 \times \mathbb{C}\textrm{P}^3$ ending on the line at the
boundary. We use superspace techniques to represent the displacement
supermultiplet and we show that superconformal symmetry determines the
four-point correlators of its components in terms of a single function of the
one-dimensional cross-ratio. Such function is highly constrained by crossing
and internal consistency, allowing us to use an analytical bootstrap approach
to find the first subleading correction at strong coupling. Finally, we use
AdS/CFT to compute the same four-point functions through tree-level AdS$_2$
Witten diagrams, producing a result that is perfectly consistent with the
bootstrap solution.
