The invariant action for solitonic 5-branes

We construct the full effective action including DBI and WZ terms for solitonic 5-branes covariant under T-duality. The result is a completion of results known in the literature to a full T-duality covariant expression. The covariant WZ action includes previously omitted R–R terms. The obtained full covariant effective action reproduces the one obtained by S-duality from the D5-brane upon the correct choice of the covariant charge.