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We study the world-volume effective action of an exotic five-brane, known asthe M-theory 5${}^3$-brane (M5${}^3$-brane) in eleven dimensions. Thesupermultiplet of the world-volume theory is the $\mathcal{N} = (2, 0)$ tensormultiplet in six dimensions. The world-volume action contains three Killingvectors $\hat{k}_{\hat{I}} {}^M \ (\hat{I} =1,2,3)$ associated with the$U(1)^3$ isometry. We find the effective T-duality rule for theeleven-dimensional backgrounds that transforms the M5-brane effective action tothat of the M5${}^3$-brane. We also show that our action provides the sourceterm for the M5${}^3$-brane geometry in eleven-dimensional supergravity

World-volume Effective Action of Exotic Five-brane in M-theory