Abstract
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 arXiv:0907.4596 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 which characterizes the strength of the interactions through the Nambu-bracket.
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