Supersymmetric M5 Brane Theories on R x CP2

TL;DR

This paper constructs supersymmetric Yang-Mills-Chern-Simons theories on R x CP2 via twisted Z_k modding and dimensional reduction from 6d (2,0) theories, matching known indices and exploring their nonperturbative completions.

Contribution

It introduces new supersymmetric gauge theories on R x CP2 derived from 6d (2,0) theories, with a discrete coupling constant and verified perturbative index calculations.

Findings

Perturbative index matches known half-BPS index.

Theories have a discrete coupling constant related to Z_k modding.

Speculation on the regimes of k relative to N for M-theory and IIA descriptions.

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