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Let $Q$ be a free Boltzmann quadrangulation with simple boundary decorated bya critical ($p=3/4$) face percolation configuration. We prove that the chordalpercolation exploration path on $Q$ between two marked boundary edges convergesin the scaling limit to chordal SLE$_6$ on an independent$\sqrt{8/3}$-Liouville quantum gravity disk (equivalently, a Brownian disk).The topology of convergence is the Gromov-Hausdorff-Prokhorov-uniform topology,the natural analog of the Gromov-Hausdorff topology for curve-decorated metricmeasure spaces. We also obtain analogous scaling limit results for facepercolation on the uniform infinite half-plane quadrangulation with simpleboundary, and for site percolation on a uniform triangulation with simpleboundary. Our method of proof is robust and, up to certain technical steps,extends to any percolation model on a random planar map which can be exploredvia peeling.

Convergence of percolation on uniform quadrangulations with boundary to SLE$_{6}$ on $\sqrt{8/3}$-Liouville quantum gravity