We study the world-volume effective action of an exotic five-brane, known as the M-theory 5${ }^3$-brane (M5${ }^3$-brane) in eleven dimensions. The supermultiplet of the world-volume theory is the $\mathcal{ N} = (2, 0)$ tensor multiplet in six dimensions. The world-volume action contains three Killing vectors $\hat{ k}_{ \hat{ I}} { }^M \ (\hat{ I} =1,2,3)$ 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 M5${ }^3$-brane. We also show that our action provides the source term for the M5${ }^3$-brane geometry in eleven-dimensional supergravity
Categories: hep-th