Non-linearly extended self-dual relations from the Nambu-bracket description of M5-brane in a constant C-field background

The derivation of the self-dual relations for the two-form gauge field in the Nambu-bracket description of M5-brane in a constant C-field background initiated in ref. [1] is completed by including contributions from all the fields in the M5-brane action. The result is used to examine Seiberg-Witten map of the BPS conditions for the string solitons, up to the first order in the expansion by the parameter g which characterizes the strength of the interactions through the Nambu-bracket.