Supersymmetric M5 Brane Theories on R x CP2

Abstract

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 $\frac{1}{g^2_{YM}} =\frac{k}{4π^2}$ 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.

24 pages, no figure, additional note for the enhancement of supersymmetries for k=2,3