World-volume effective action of exotic five-brane in M-theory

We study the world-volume effective action of an exotic five-brane, known as the m-theory 53-brane (m53-brane) in eleven dimensions. the supermultiplet of the world-volume theory is the $$ mathcal{n}=left(2, 0right) $$ tensor multiplet in six dimensions. the world-volume action contains three killing vectors $$ {widehat{k}}_{widehat{i}}^m $$ (ȋ = 1, 2, 3) associated with the u(1)3 isometry. we find the effective t-duality rule for the eleven-dimensional backgrounds that transforms the m5-brane effective action to that of the m53-brane. we also show that our action provides the source term for the m53-brane geometry in eleven-dimensional supergravity.