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We use an exact mapping of the Manna model, or equivalently conserveddirected percolation, onto disordered elastic manifolds at depinning to showthat particle-density fluctuations in these two models are hyperuniform. Thestructure factor of the particle density behaves for small $q$ as $S(q)\sim|q|^\sigma$ with $\sigma={4-d-2\zeta}$, where $\zeta$ is the roughness exponentat depinning. In dimension $d=1$, $\sigma=1/2$, while for all dimensions $0.6>\sigma\ge0$. Our results fit well known simulations in the literature, exceptin $d=1$, where we perform our own simulations to confirm our findings.

Hyperuniformity in the Manna Model, Conserved Directed Percolation and Depinning