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 N=2,0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=\left(2,\ 0\right) $$\end{document} tensor multiplet in six dimensions. The world-volume action contains three Killing vectors k^I^M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\widehat{k}}_{\widehat{I}}^M $$\end{document} (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.