Supersymmetric M5 Brane Theories on R x CP2

We propose 4 and 12 supersymmetric Yang-Mills-Chern-Simons theories on R×CP2 obtained by twisted Zk moddings and dimensional reduction of the 6d (2,0) superconformal field theories on R×S5. These theories have a discrete coupling constant 1g2YM=k4π2 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 Zk modding of the AdS7×S4 geometry, we speculate that the M region is for k≲N1/3 and the type IIA region is N1/3≲k≲N. When nonperturbative corrections are included, our theory is expected to produce the full index of the 6d (2,0) theory.1120sciescopu