In this paper, we construct a sequence $(c_k)_{ k\in\mathbb{ N}}$ of symplectic capacities based on the Chiu-Tamarkin complex $C_{ T,\ell}$, a $\mathbb{ Z}/\ell$-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 $T^*X\times S^1$. We define a sequence of "contact capacities" $([c]_k)_{ k\in\mathbb{ N}}$ on the prequantized contact manifold $T^*X\times S^1$, and we compute them for prequantized convex toric domains.
Categories: math.SG