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The derivation of the self-dual relations for the two-form gauge field in theNambu-bracket description of M5-brane in a constant C-field backgroundinitiated in arXiv:0907.4596 is completed by including contributions from allthe fields in the M5-brane action. The result is used to examine Seiberg-Wittenmap of the BPS conditions for the string solitons, up to the first order in theexpansion by the parameter $g$ which characterizes the strength of theinteractions through the Nambu-bracket.

Non-Linearly Extended Self-Dual Relations From The Nambu-Bracket Description Of M5-Brane In A Constant C-Field Background