  We propose 4 and 12 supersymmetric Yang-Mills-Chern-Simons theories on
$\mathrm{R\times CP^2}$ obtained by twisted $\mathrm{Z}_k$ moddings and
dimensional reduction of the 6d (2,0) superconformal field theories on
$\mathrm{R\times S^5}$. These theories have a discrete coupling constant
$\frac{1}{g^2_{YM}} =\frac{k}{4\pi^2}$ so that instantons represent the
Kaluza-Klein modes correctly. We calculate the perturbative part of the SU(N)
gauge group Euclidean path integral for the index function and confirm it with
the known half-BPS index. The scalar and fermionic fields have the conformal
dimension prescribed by the 6d theory. From the similar twisted $Z_k$ modding
of the $\mathrm{AdS_7\times S^4}$ geometry, we speculate that the $M$ region is
for $k\lesssim N^{1/3}$ and the type IIA region is $N^{1/3}\lesssim k \lesssim
N$. When nonperturbative corrections are included, our theory is expected to
produce the full index of the 6d (2,0) theory.
