More on the Nambu-Poisson M5-brane theory: Scaling limit, background independence and an all order solution to the Seiberg-Witten map

We continue our investigation on the Nambu-Poisson description of M5-brane in a large constant C-field background (NP M5-brane theory) constructed in refs. [1, 2]. In this paper, the low energy limit where the NP M5-brane theory is applicable is clarified. The background independence of the NP M5-brane theory is made manifest using the variables in the BLG model of multiple M2-branes. An all order solution to the Seiberg-Witten map is also constructed.