Capacities from the Chiu-Tamarkin complex

In this paper, we construct a sequence $(c_k{)}_{k\in \mathbb{N}}$ of symplectic capacities based on the Chiu-Tamarkin complex $C_{T,\mathrm{\ell }}$, a $\mathbb{Z}\mathrm{/}\mathrm{\ell }$-equivariant invariant coming from the microlocal theory of sheaves. We compute $(c_k{)}_{k\in \mathbb{N}}$ for convex toric domains, which are the same as the Gutt-Hutchings capacities. Our method also works for the prequantized contact manifold $T^{\ast }X\times S^1$. We define a sequence of “contact capacities” $([c{]}_k{)}_{k\in \mathbb{N}}$ on the prequantized contact manifold $T^{\ast }X\times S^1$, and we compute them for prequantized convex toric domains.